Yeah it'll play all DS games. Well, apart from ones that need the GBA slot, but there's only one that I can think of that uses that.
DS recommendations... I actually had a paragraph of stuff typed here, but I realized I could go on for ages because there really are loads, so I'm going to be lazy and post these links;
http://www.neogaf.com/forum/showthread.php?t=222049
http://www.neogaf.com/forum/showthread.php?t=725449
Yeah, it's Neogaf, but for those kind of threads it's pretty useful.
They should keep you busy for a while.
I'll quickly list a few of my favourites though;
Castlevania: Dawn of Sorrow
Kirby Super Star Ultra
Professor Layton and the Curious Village
Yoshi's Island DS
Resident Evil Deadly Silence
Contra 4
Pokemon Heart Gold
New Super Mario Bros (if you've played any of the others, maybe give this a miss, but if not give it a shot)
Worms Open Warfare (I don't know why I like this, it's just Worms, but I've played it absolutely loads)
Chrono Trigger
There's 10 to start with. If you want any more specific type/genre recommendations then just ask!