OK here's some apps I've been using on my Nexus 7. Not all are optimised (yet) but some will be soon (I'll note if that's the case). In almost every case these apps follow the new Android design guidelines. Some are tablet optimised or have versions on the way soon. I've only tried to include apps where the performance (smoothness, responsiveness) matches up to my expectations of a modern Android app. If you like it, let me know and I can maybe add in more. I haven't really included games either!
Safe In Cloud
Awesome Password manager/backup service which uses the cloud sync between your Android Devices. Desktop version coming September 2012. I use it all the time.
Pattrn
Lovely app, great if you like patterned wallpapers.
Timer
Really simple, but beautiful Timer.
https://play.google.com/store/apps/details?id=com.laurencedawson.reddit_sync.pro
The best Reddit client on the play store. Dev is super responsive (on Reddit). Currently on version 6, Tablet UI coming in version 8.
Clipper
Great way to manage the Android clipboard. Really useful if you need to copy and paste multiple but separate items.
Reader HD
Great RSS reader. tablet optimised. Has a magazine layout too.
Boid
This isn't yet available to download for the Nexus 7, but the next release will be (in the next few days). Great Twitter client. Still in Beta but unbelievably smooth. Version coming in the next few days will include auto complete of user names, push notifications and lots of other stuff. Tweet caching and a tablet UI should hit within weeks. Makes the official Twitter app look like the pile of crap it is.
Evernote
Evernote. Tablet optimised. Syncs notes in the cloud. Awesome.
Google Translate
Really useful for translating Tweets and the like. You can also use this for web pages in Chrome. Chrome > Share page > choose translate > Bingo. Only seems to work with desktop sites.
Soccer Livescores
Love football? Best football scores app hands down. Notifications for goals scored, can set favourite teams and loads more.
Tasks
Awesome task manager which syncs in the cloud using Google tasks. Great widget , tablet optimised in landscape.
Battery Widget Reborn
Battery Widget(s), super stylish. tablet optimised.
Dropbox
It's dropbox. Totally awesome.
Evernote Food
Like Evernote, but for food. For those of you who eat out a lot, or fancy yourselves as chefs/
Guardian Crosswords
It's a Crossword app. But ICS style.
Google Drive
Drive. Alternative to DropBox but with 5GB free storage and syncs with google docs. As my work literally lives in Google Docs it's invaluable.
MD.emu
Megadrive emulator. Grab a USB OTG cable for your PS3 controller and you've got the worlds best Megadrive/Genesis emulation device at your fingertips.
Snes9x
See MD.Emu but for Snes. Not available on the play store, but you can download it for free at the Devs website.
IMDB
IMDB. Tablet optimised.
Lobowiki
ICS style Wikipedia browser. Still very early Beta.
DealPad
UK only. Hot UK Deals for your tablet. Looks great.
Notes With task Sync
If you need to take Notes, but want something lighter than Evernote, use this. Syncs in cloud with Google Tasks.
Spotify
The new Spotify Android app is a thing of beauty. Not tablet optimised but works great on the Nexus 7.
Imgur
Post on any kind of forum? You need this app. Notifications are JellyBean optimised!
Folder Sync
Foldersync. Allows you to sync any folder on your phone/tablet with your choice of cloud provider. Works great.
Flipboard
It's flipboard. Not tablet optimised.
InstaWifi
InstaWifi allows you to share Wi-Fi passwords by NFC or QR code. Makes sharing Wi-Fi passwords a doddle.
Solid Explorer
One of Androids best, if not the best file explorer.
TED Talks
TED talks. Tablet optimised.
Tune In Radio Pro
Colors
Simple wallpaper app allowing you to set a plain color as your wallpaper.
Foursquare
Foursquare. Not tablet optimised but looks great anyway.
Markers
Tablet optimised sketching app. Simple but elegant.
Movies
Movies. It's not properly optimised for &" yet as the text is wonky in portrait, but it's fine in landscape. Great for checking movie times/theatres etc etc
Trivialist
Awesome trivia app which allows you to challenge your friends. Dev is currently working on optimising for tablet.
Beyondpod
Not totally sold on the UI yet, but probably the best Podcast app on the play store.
Aircalc
Aircalc. One of these floating apps that are better suited to tablets than phones. Try it.
Stick It
Same as aircalc but for videos. Similar to the feature Samsung tout on the S3 which allows you to watch videos whilst web browsing etc
Tablet talk
Hooks up to your android phone so you can send texts from your tablet and receive them instead. Useful when your phone is on charge and you'd rather use your tablet.
Jotterpad HD pro
Another note taking app, with a nice UI
OK that's it for now. There are many, many more that I've missed. If people think it's worthwhile I'll go back and add some more in.