I've been learning for about two months. A good beginners' song is 'Yellow' by Coldplay. It's the first song I learnt to play. There aren't any tricky rolls, it's pretty straight playing but it is dynamic too, with use of both the hats, ride and crash cymbals. Also a bit of variation on the kick drum in the choruses, which isn't too difficult.
'Living on a Prayer' by Bon Jovi is another one I'm looking at. A bit more technical and faster in tempo, with some rolls, but pretty straight drumming.
I'm learning 'Come Together' by the Beatles at the moment and it's really cool - introduces you to some more rolls including triplets, and some ghost beats. And it's just got a good bluesy groove to sit back into. Although, Ringo's patterns are a little wacky at times, but you can adapt them around the drum kit to make it feel more natural to you.
I generally just stick on my Ipod and try and play along to whatever is playing. This encourages me to express a bit of creativity instead of just reading drum music or playing a piece beat for beat, and it gets you familiar with different feels.
I downloaded a fair bit of drum music from the internet - it's out there if you're into that kind of thing. I want to learn 'Creep' next by Radiohead.
Let us know what you're playing. It's always good to get ideas as a beginner.