The easiest strumming song ever has to be "Name" by goo goo dolls. The trick to the song was they used some really weird tuning so all the chords use the fingering 0-0-0-0-0-0 or 0-2-2-2-2-2 (I believe, been forever since I've played it, but it's very similar to this) and just change the strings they strum.
-Chu
EDIT : Bullet with Butterfly Wings by the smashing pumpkins is also really easy to play but sounds really hard. Everything based around 0-2-2-0-4-x and 0-0-0-0-4-x with another weird tuning, and it sounds much harder to play then it is. If you want to try a very easy non strumming song that sounds hard, try "Heaven Beside You" by Alice in Chains.