Not system tools (which hopefully is the reason you're asking this for one of the top 3 systems for homebrew):
- Wii Earth (online map viewer, some sources are dead but others still work)
- 240p test suite (video test pattern generator AND toy for when you're stoned)
- RSSMii (does it really count when it basically only configures a server side job? Still, I have a bunch of blog posts that survived on the NAND backup of my first console...)
- Achtung Wii Kurwe (PC game adaptation, but one that I like AND you don't seem to see on every single modded console)
- Syobon Action Wii (ditto)
- Schism Tracker (if you know the name you'll know why you want it, else you probably won't care )
- A media player, can't decide between WiiMC, WiiMC-SS, and MPlayer CE, all have their strengths and all are beaten by XMBC on the first Xbox
- FMyLife and Wii Twitter were nice but have been broken for at least 10 years...
Utilities:
- Some YAWMM Mod (title installer)
- BlueDump Mod (title exporter)
- AnyTitle Deleter Bushing version (title remover)
- Priiloader (should have been #1 on the list lol)
- Nintendont and Configurable USB Loader
- Savegame Manager GX (last on the list because, like pretty much every console UI knockoff, it's crappy - GENERALLY does its job though)
Emulators (last because you can do much better = accurate on a modern computer, if you want to get proper TV out with limited hassle though...)
- mGBA (VBA GX as a very distant second choice in general, but nice for titles with gimmicks)
- FCE Ultra GX
- Genesis Plus GX