I'm thinking of the DS and Lite here, not the DSi, which some of this doesn't apply to, but:

Internet capability built-in.
MP3 playing.
Internet radio.
Photo storage.
Downloadable games that don't require a physical copy.
Looks WAY cooler.
Tiny analog stick rox. ^_^
Skype.
You can download movies and TV episodes off the PSN.
Better games- the only ones I have are Dissidia and Crisis Core but I like them better so far than any of my DS games.

...Need I go on?