from off the top of my head, it's called shaky camera method
there's Rachel Getting Married, The Bourne Ultimatum, Baghead, Friday Night Lights, The Celebration, and The Idiots.
[editline]12:09AM[/editline]
also, blair witch
The blair witch project.
The Last Exorcism, Invisible Monsters.
[media]http://www.youtube.com/watch?v=V_-gL3U1T5Y[/media]
This is coming out soon. Sorta has that Cloverfield vibe to it.
For Handheld camera movies, Quarantine was a remake of foreign film, REC which has a sequel REC2.
[media]http://www.youtube.com/watch?v=qGCzbvfFO4Q&translated=1[/media]
There was also Diary of the Dead by George A. Romero. One of his zombie films all shot by a small group with a hand camera through the entire film.
[media]http://www.youtube.com/watch?v=JS_JQsljVlI[/media]
District 9. Great filming IMO.
Monsters coming out this year looks like its going to have a similar camera style/atmosphere.
[media]http://www.youtube.com/watch?v=D5_nKDwR4sk[/media]
Ninja'd!
Go see Let me in, it is really good.
If you liked Quarantine, make sure you have seen the original REC.
I personally love handy cam movies. Don't know why. I just like the feel of them.
The Zombie Dairies was pretty good, It was an indi film that turned out to be a great watch.