Currently dominated by Netscape, Mozilla and FireFox on the windows platform, a capable and nice group of browsing software. Now that Netscape has died, and Mozilla as an application suite too, that leaves FireFox as the dominant gecko browser for the future.
Gecko based browsers can roughly be split in two categories: the XUL browsers and the native browsers.
XUL browsers are the Mozilla Application Suite, moribund Netscape 6/7, and Firething, native browsers include K-Meleon, Galeon, Chimera.
The difference between the two categories is that XUL browsers use the proprietory XUL language to write their entire interface and thereby are platform independant, whereas the native browsers use elements from the operating system. The native browsers are a lot faster and more stable because of that reason, but they are not always using the last version of the Gecko engine.