There are a couple I've recently downloaded (though maybe not all today):
I've downloaded Feedly, to get me the news from different sources all in the same app.
Defenders is a free game that has kept my attention longer than any other iOS game. You have the option to buy in-app additions, but I've been able to play a ton without spending a nickel. Its a 'Tower Defense'-type of game, and its pretty dang fun.
RemoteMouse lets me use my iphone as a mouse to my Mac, which is really nice when I put a movie on my computer, then hook it up to my TV. I can use all the controls (play, pause, rewind, etc.) from my seat, rather than going up to my computer to use those functions. Very handy.
I'm also a big fan of the Yahoo! Weather app, as it has a nice widget that I can view from the pull-down notification screen (I don't use the actual app, it sits in a folder on my last screen).