What does and does not work (most likely all works but here it is!) Post what you have / have not got working and I'll try to keep on top and update the first post.

Works
Winterboard
Categories
OpenSSH (successful transfer from pc)
Terminal
Weather Icon
Reflective Dock (App version)
Privacy
Safari Download Manager (paid app)
AptBackup
SBSettings
iFile
Free Ram
MIM (Make it Mine)
FiveRows
Steffwiz --> All Sources (Repositories)
iCommander
PDANet (over USB)
dTunes
MXtube
UserAgent (SB Toggle)
SDM (SB Toggle)
iPod (SB Toggle)
5ColumnSB
5IconDock
Dock
snes4iphone
NES (unconfirmed)
iPodPop

Doesn't Work
GPSphone
StumblePlus

Issues (may / may not work)
Springjumps
MobileTerminal (Temperamental)
Notifier (Read warning below)
Supreme Preferances (Will not install via Cydia, if you have a copy you can SSH it over, UI issues but gernally works)
Rock (on blackra1n might mess your iPod up..)

WinterBoard
>Keyboard skinning - DOES NOT WORK (Since 2.2.1)
>Springboard background's and dock - Work
>Springboard icons - Work
>Email sounds - Work
>Unlock / lock sounds - Work
>UI Skins (eg matte graphite) - Work

Problems on 3.1.2
>If you install Notifier, it may break Cydia. If you have already installed do not fear, navigate to "/var/lib/dkpg/updates" and delete the contents of this folder and Cydia will work again! (This has been an issue since the newest update)
>Cannot access everything (on root) but SSH still works in "/var/media" with Disk Aid 3.1
>Hiding Icons - may not hide the icon but apps such as Categories still work
>Cydia crashes (mainly due to low memory - not as such an issue with 3GS and iPT 3G)
>Word of warning about AptBackup, if you had problems with your previous jailbreak (eg cydia would crash on start like mine would) and you use AptBackup it may carry those issues over, if you had problems avoid having to re-jb and do not use AptBackup!

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IMO - If you want an app and it does not work, leave it installed and wait for a update to trickle through. I doubt it would require anything more than a line of code to be altered to get something to work, unlike 2.2.1 to 3.0 which required some major re-writes.