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A few I recommend are:
Google Chrome, my favorite Web browser by far
SwiftKey, and there are several keyboards but I dislike the stock one
Power amp, best music player app in my opinion
Teamviewer, free way to access any pc from your phone
Nova launcher, this is my favorite of the ICS+ launchers, and never been a big fan of touchwiz.
Edit:
A few I forgot are the xfinity player if you have comcast as a cable provider
Dropbox, a good way to keep files synced between many devices/computers
Also Google drive, and for the same reason as above
Yea AVG and lookout have these too, among loads of others.My favorite app is Avast for its anti theft features.