I haven't chosen a case yet. I can't decide between the DodoCase, the inCase Convertible Magazine and the inCase Convertible Book.
As far as apps go, here are my favorites so far:
APPS:
Dropbox - Cloud-based file storage; has Windows, Mac, Android and iOS clients. THE best way to get files in/out the iPad
Kindle - Amazon's eBook reader software. Syncs across platforms (Mac, Win, iOS, Android)
GoodReader - Document reader. Has built-in Dropbox support
Evernote - Cloud-based document manager. Great for notes, scans, photos, etc. Syncs across platforms (Mac, Win, iOS, Android)
1Password - Password-manager. Has built-in Dropbox support and Windows, Mac, iOS, Android clients
Friendly - A nice Facebook client
Reeder - RSS reader that syncs with Google Reader
Twitter - Twitter client
Wikipanion - A nice Wikipedia client
Pandora - Streaming music
Netflix - Movie-watching client, only useful if you have Netflix (or are willing to get it)
Adobe Ideas - Nice little sketching app
Instapaper - Web-page read-it-later tool
GAMES:
Angry Birds
Cut the Rope
Plants vs. Zombies
Fruit Ninja
Carcasonne
Things I haven't checked out yet, but will soon:
Infinity Blade - RPG
Rage HD - shooter on rails game
iThoughts HD - mind-mapping app
Papa Sangre - no-video video game
Elements - Dropbox-based text editor
Pages - word processor
Keynote - presentation app