Here's what I'm looking for :
1) RPG (turnbased / pseudo realtime)
2) platform / action game
3) quirky / fun game
Based on what your looking for, I'd recommend either Castlevania
or Mario & Luigi : Partners in Time.
I had never played much Castlevania before, but the DS version has me hooked. The top screen is great for the map, but not much else. Touch screen functionality feels a bit tacked on, but it's not really an issue.
M & L surprised me with how fun it is. I've put a few hours into it and it's could actually fill all three of your criteria. The top screen is used to control the babies while the bottom is used for the normal M&L. The two are often used in conjunction when they are separated, otherwise it's mainly used as a map. I didn't play the first one, so I can't compare the two.Animal Crossing
will eat your time like nothing else.
But aside from those, if you like rhythm games at all...Ouendan