Both Days of Ruin and Dual Strike are good games, but I'd say Dual Strike is better if you like single player while Days of Ruin is better for multiplayer. The primary reason for that is that in Dual Strike you can get ridiculously overpowering combos which, when playing another human, just doesn't seem fair.
As for other games along the same lines (Turn based strategy), I'd suggest looking at Disgaea DS, Fire Emblem, and Final Fantasy Tactics A2.
Another type of game worth a look are the rougelikes. They're RPGs where you travel around randomly generated dungeons trying to complete assorted objectives, but also have a challenge in which if you die in the dungeon, you lose a good chunk of equipment. They make excellent games for the DS as they're the type of game where you can play in quick bursts of a few minutes if desired. The primary games for that sub-genre for the DS would be Shiren the Wanderer, Izuna the Unemployed Ninja, and Pokemon Mystery Dungeon.
Just wanted to say thanks for the game suggestions. I already have pokemon and have been looking into getting some of the mario games. I had never heard of Advance Wars before and it looks good. I think I will be picking it up. Would you recommend getting the newest one?