The best macro photography is achieved with dedicated macro lenses. However, while travelling one does not necessarily want to carry an extra lens around. So, close-up lenses or extension tubes can be handy.

For macro photography it is useful to remember the lens formula for a simple thin lens:

1     1      1
-  =  --  +  --
f     Od     Id

where f is the focal length of the lens, Od is the distance from the object to the lens and Id is the distance from the image to the lens. The total distance from camera to object would be D is Od + Id. The magnification M is Id / Od.
At a 1 : 1 magnification the object is the same size as the image, and therefore Od is equal to Id. From the formula above follows that for a 100mm lens Id and Od equals 200mm (2 x f), and the total distance from camera to object D is 400mm.
The Canon FD 100mm f/4.0 macro lens behaves very much like a simple thin lens. The lens itself extends substantially, and an extra extension tube of 50mm is necessary to allow the lens to go to 1:1 magnification.
More modern macro lenses such as the Canon EF 100mm f/2.8 USM macro use internal focusing, so they do not extend like the Canon FD 100mm f/4.0. Therefore, it should be noted that especially for wide-angle zooms and lenses with internal focusing, the above formula may be a poor approximation, it depends where the nodal point within the lens is (i.e. the point that would correspond to the ideal simple thin lens). Nevertheless, from the formula above follows the principle that extension tubes are more effective with shorter focal lengths, i.e. simplistically you need a 24mm extension with a 24mm lens to reach 1:1, a 50mm extension for a 50mm lens and a 200mm extension for a 200mm lens.

 Brief comparison of different close-up/macro methods (excluding macro lenses)

Close-up lenses

Close-up lenses are a simple alternative to obtain additional magnification with a normal lens. When you place two lenses (simple thin lens approximation) next to each other the combined focal length is:

1     1      1
-  =  --  +  --
f     f1     f2

Close-up lenses are labeled with their diopter values, e.g. +1, +2, +3, etc. This can be converted to a focal length by dividing 1 meter with the diopter value: a +2 lens is 500mm (1000 mm / 2), or a +4 lens is 250mm. If you take now any lens focused to infinity and add a +4 diopter close-up lens the focal point will now be at 250mm from the front of the lens, i.e. the focal point of the close-up lens. Combining a +4 diopter lens with a 250mm lens gives a combined focal length of 125mm from the formula above. Given that the distance from image to lens is 250mm and from lens to object is also 250mm, we have now a 1:1 magnifcation with this combination. With a 50mm lens and a +4 diopter close-up lens you get a combined focal length of 41.7mm, and a magnification of 1:5 (50mm to 250mm). Note that this does not include that you can focus with the lens itself closer. Of course you will be able to get a higher magnficiation with a close-up lens on a 50mm depending on how close the lens itself can focus. But generally speaking, in contrast to extension tubes, close-up lenses work more effectively at longer focal lengths.
Close-up lenses can be obtained as simple lenses from, e.g., Hoya. However, there are also achromat constructions consisting of 2(-3) lenses that reduce chromatic aberations. Achromats usually give better pictures, especially at higher diopter values, and are recommended.

Achromat close-up lenses:
Canon 250D +4 diopter (focal length 250mm)
Canon 500D +2 (focal length 500mm). This lens is coated, see transmission curve here.
Raynox DCR-250 +8 (focal length 125mm)
Raynox DCR-150 +4.8 ( 210mm)
Marumi DHG Achromat Macro 330 (+3, 330mm)
Marumi DHG Achromat Macro 200 (+5, 200mm)

Examples of magnifications achieved with the Canon 250D and 500D close-up lenses:

See also Bob Atkins' macro discussion, and his table of the Canon 250D and 500D in combination with various lenses, as well as the EF 12 and 25 extension tubes. Canon also has a nice write-up and table of magnifications with the 250D and 500D close-up lenses.
At the lensmate site you can find comparisons of different close-up lenses on different pro-sumer compact cameras, e.g. Powershot S5, or Canon Powershot G9. This will give one a general overview of magnification and quality of different close-up lenses.

Inverted (reversed) lens as a close-up lens together with a normal lens

A special case of a close-up lens is if one uses another lens as a "close-up lens". You can buy male-male filter lens adapters that allow you to mount a second lenses inverted on the camera lens. Effectively the second lens works like a close-up lens. A 50mm prime lens acts as a +20 diopter close-up lens. If both lenses are focused to infinity the working distance from the back of the lens to the object is the distance that the lens normally has from the lens mount to the image plane (around 45 - 50mm depending on camera brand and mount). Such a setup up is probably not recommended if your main lens has a plastic mount or plastic filter threads, due to the extra weight attached to the front. Also, depending on lens combinations, vignetting will be a major issue. I have briefly tested a Canon 50mm f/1.4 lens with a Canon FD 24mm f/2.8 as close-up lens and vice versa. Both combinations give severe vignetting, you see a round circle in black. I then tried the Canon FD 70-210 f/4.0 with the 50mm f/1.4 as close-up. At the 210mm tele position, the setup would be usable with some darkish corners, and it has a high magnification ~ 3:1, at 70mm it shows circular vignetting. Hence, you need a lens with a small front opening or a tele lens, combined with a rather large open diameter lens as close-up. Probably the most useful combinations are small prime lenses with metal mounts or use this set-up on prosumer cameras which have smaller lenses.

Extension tubes

From the magnification formula above it follows that extension tubes are one way of increasing magnification by moving the lens further away from the camera body. Their effect depends on the lens they are used with and the length of the tubes. Longer tubes and/or shorter focal lengths will give higher magnifications. Thus, in contrast to close-up lenses, extension tubes work most effectively at shorter focal lengths. But like close-up lenses one cannot focus to infinity anymore.
Canon offers two extension tubes: Canon EF 12 II and Canon EF 25 II extension tubes, both with o-rings for weather sealing and the work also with EF-S lenses. 
Here are some lens examples with magnifications obtained with the extension tubes, taken from the Canon Web site (Canon.de):

Another Canon list is viewable from Canon. As can be seen, extension tubes give higher magnifcations with shorter focal lengths. * While canon.de gives these values, canon.jp and users at dpreview showed that only the 12mm tube is usable with the lens at 22mm. ** for this lens there is conflicting information from Canon (.jp vs .de); it should be noted though that with the wide-angle lenses you will most likely be focusing very close to the front lens or inside it, hence usability is restricted.

There are a number of extension tubes also from third parties, although one should verify that one gets more recent versions which are compatible with EF-S lenses. The Kenko extension tube set with three tubes (12, 20, 36mm) and electronic contacts is popular, and since about 2008 also compatible with EF-S lenses.

Here is a nice example of Kenko's extension tubes on a 70-200 zoom by Doug Smith, showing that one can have higher magnification at the shorter focal length. Macro shots with a Canon 50mm f/1.8 and extension tubes by Charles Durrant .

Bellows as Extension

A "flexible" version of extension is provided by a **macro bellows** . However, most of these are from the days of 35mm film and meant to be used with manual focusing. Canon, for example, does not make an EOS/EF compatible bellows. Novoflex builds bellows and also provides a linked pair of adapters that have the EOS electric contacts, so aperture control and autofocus is possible. Bellows often provide also means of reverse mounting of lenses, see below.

Reverse mounted lens

When aiming at high magnifications with extension tubes or bellows, the lens can be reversed - if it is a normal type lens (e.g., a 50mm f/1.8) since the distance from the image becomes now larger than the distance to the object. Therefore optical quality is improved. You can get reversal rings to mount a lens in reverse position on - for example - extension tubes. Disadvantage: you have to adjust everything manually (unless you use an - expensive - option like provided by Novoflex, see above). More recently, Meike and Kooka also provide automatic lens reverse adapter rings for reasonable prices.

Minimal working distance (MWD)

The minimal working distance, i.e. the distance from the front of the lens to the object, is an important aspect of macro photography, since you don't want to scare insects, and leave enough room for light.

*actual measure working distance at minimal focus, which is less than 0.2 and gives a higher magnification of about 1:2, see below in wide-angle macro.

For working distances (in cm) for a standard 50mm lens with Kenko extension tubes, see table above.

Generally though, also derived from the first formula above, the working distance should never become less than the focal length minus the distance from the nodal point of the lens to the front of the lens. Therefore, tele lenses have longer working distances. The same applies to dedicated macro lenses: the longer the focal length, the bigger the working distance. The digital picture has a list of working distances for different macro lenses.

DOF (depth of field)

At high magnifications DOF becomes very small. On crop cameras apertures of up to f 16 can be used to increase DOF, but larger than that diffraction starts to affect lens performance substantially. At high magnifications, e.g., 1:1, DOF is not dependent on focal length, and hence close-up lenses do not give a smaller DOF than macro lenses at the same magnification. The Holding Tank has CoC plots for different focal lengths and magnifications.

Macro lenses

Macro lenses are obviously the best choice. But to travel light, or on a budget, the extension tubes and/or close-up lenses are viable options for the occasional picture. And in some instances using an extension tube with an excellent lens such as the Canon 70-400 f4 IS allows you to get closer than the minimal focusing distance, but still have a large working distance.
Modern macro lenses are designed to give 1:1 magnifications, so called life size magnification, i.e. a 1cm diameter coin will be 1 cm in size on the sensor. Older macro lenses (E.g., Canon 50mm f/2.5 macro from 1987, but still in the line-up as of 2012, or the current Zeiss 50mm f/2 and 100mm f/2 macro planars ) only go to 1:2, i.e. half life size. One needs an extension tube (or Canon sells a rather expensive life-size converter for the 50mm f/2.5 macro) to go down to 1:1; this used to be normal in film days before autofocus lenses.
The digital picture has comparisons of different macro lenses.

"Pseudo-macro" lenses

A number of manufacturers stick a "macro" label on their lenses, when a lens can achieve a relatively "good" close-focus. These are mostly all-around zooms, although Sigma also has a few primes. They are not real macro lenses specifically designed for macro work, they are just normal lenses that can focus closer. Canon does not put such a macro label on their lenses, although they designate lenses that can do relatively high close-focus with a flower symbol. So, before falling into the "macro" trap, one should look at the magnifications achieved in the technical specifications. Some examples show that Canon lenses, although not marked with "macro", compare well with other brands that are labelled "macro":

Wide-angle macro

One will notice that most macro lenses offered start with a focal length of 50mm. The current exception is the Tokina/Pentax 35mm macro, made for APS-C (equivalent field of view of a 50mm on FF), but it's discontinued. Canon introduced a EF-S 35mm macro for APS-C in 2017. Lenses starting from about 50mm are easier to design because of the flange distance of the dSLR mounts. An important aspect is working distance at macro magnifications, which is a function of focal length. With wide angle lenses you could be so close (or even inside) the front lens, that working and lighting is not possible. So the choice of starting with about 50mm for a macro lens is not surprising. Also one can simply consider the diameter of the front element of a wide-angle lens. Because of the large exit angle, these front elements can be quite large, often larger than the size of a sensor. Hence, even something stuck to the front of the lens will never be reproduced at 1:1. So, achieving a wide-angle macro look with a dSLR is not easy. P&S cameras have an advantage here, due to the small sensor and lack of mirror box.
In the list below I measured the approximate working distance of the Sigma 17-70 macro and Canon 18-55 IS which have close-up capabilities. What magnifications are possible at shorter focal lengths? Also, an old FD 24mm f2.8 lens is used with an FD-EOS macro adapter, which works like an extension tube. The adapter is 10mm, but since the flange distance of FD lenses is 2mm shorter than EOS lenses, the effective extension is 8mm. Some Sony P&S cameras are also compared. They can give really high magnification.

*The minimal focusing distance of the Sigma 17-70 is somewhat below the 0.2 spec given (probably for the AF to be able to bracket), so a higher magnification can be achieved, but the working distance is useless. With a working distance of 40mm, a magnification of 1:2.56 is achieved. Note that the turn of the focus ring from about 0.19m to 0.23m is very minimal, but causes dramatic changes in working distance.
As can be noted the Sigma 17-70 macro and Canon 18-55 IS do not give such high magnifications anymore when used at the wide-angle position. The manual Canon 24mm lens gives much higher magnification with extension tube. The most reasonable way to get macro-like capabilities is to take wide-angle lenses and combine them with a short extension tube (e.g. a 12mm, alas no shorter ones are available).
User brightcolours at photozone and dpreview is using extension tubes with wide-angle lenses to achieve wide-angle close-ups, look for his galleries.
** here applies a conversion to FF sensor size, i.e. how much magnification would you need on a FF camera to get the same frame filling magnification (horizontal direction).

Focusing

At high magnifications such as 1:1, focusing is best performed by moving the camera back and forth, rather than turning the focusing ring on manual focus lenses. In fact, at magnifications of 1:1, changing the focus affects the magnification more than the focus (This is also a consequence of the formula at the top). That is why bellows have two rails, i.e. one for changing the extension of the bellows (to set magnification, rather than the focus), and a second one that moves the whole setup back and forth, which is mainly used to focus.
Bellows are little used these days, but focusing rails are still useful for macro work, see for example here .

More stuff on close-up lenses:

test of Marumi 330 on a 80-200 f2.8, not so great result.
Canon on Extension tubes, Canon on close-up lenses, Canon on macro lenses
Close-up calculations with online calculator
http://www.cs.mtu.edu/~shene/DigiCam/User-Guide/A95/Close-Up/Close-Up-Lenses.html
Close-up and magnification formulas
More calculations and nice tables for Nikon lenses
Wayne Schmid's close-up and extension tube , and Canon MP-E 65 mm macro guide
Little macro stand that attaches to front of lens
The Holding Tank on macro
8 macro lens comparisons
Cambridgeincolour on extension tubes and close-up lenses