I know they're not according to the rules, but I'm still going to start by mentioning ohneswanzenegger, wii backup manager, uneek+DI, modmii, mighty channels and (especially) postloader. They may not be traditional homebrew apps, but it would be a shame NOT mentioning them.
But to the traditional applications:
10. SDL mame (just for the awesome games...the emulator in itself is just a "it gets the job done" one).
9. savegame manager gx (only really used this to copy my savegames to uneek...but that by itself is enough to get mentioned)
8. MMM (dop-mii and wiimod get honorable mentions, but this one seems to work best under uneek)
7. scummVM
6. Descentwii
5. WiiMC
4. RawkSD
3. genesis plus gx
2. Swiss
1. Tantric's emulators (FCEUGX, VBAGX, SNES9X)