I don't know what kind of apps you are looking for so I'll just list the apps I use often
(I own a Galaxy Note II I don't have stock android ICS)
Google Chrome Browser - better than any browser I have used on android, you will enjoy Chrome to phone.
Amazon Kindle - my phone is great for reading so I try to get books on Kindle instead of on apples ibooks
Bamboo Paper - works great for note taking and quick sketching, you don't need a stylis to enjoy.
Andy-83 - Best Graphing calculator app I have ever use.
Barcode scanner - a must for all android users.
Google Drive/ dropbox - great for moving files to and from your computer and phone.
Flipboard - its like a personal magazine with great layout and pictures.
Google + - I just discovered the community feature and wow it looks VERY nice on my phone. I plan to start using it more often. Style Savy Trendsetters Community is very active so I'm thinking more popular subjects will be even more active.
Linked in app - great to keep up with you profile if you have one
Netflicx - works great
Real Calculator - best basic calculator I've found
Snapseed - free photo editor with lots of options
Ove - A timer that is very easy to operate and looks like it was designed by a graphic designer.
Adobe Reader - for pdf reading