Is a DS worth getting?
What are the most popular games for its? 
Yes (I think so)
Offhand; Mario Kart DS, Animal Crossing (the gaming equivalent of a nice cup of tea), Advance Wars DS (great TTS), Brain Training (it's sums, yet fun!). Popularity, mind. It kind of depends how much you like the interface I guess; stuff using the stylus primarily is probably a matter of taste / comfort, and you're always best looking at loadsa reviews and trying a loan of one.
so wait, does the new DS lite have a web browser included?
There's a version of Opera under development (I think with Java but not flash support...or is it the other way round?). No word on release outside of Japan AFAIK. Plus there is some media stuff due from 3rd parties too, to play movies and mp3s.