This is personal experience, but I think I'll pass the words along to those that want to make a decision on what gaming system to buy or perhaps a present.
I got my DS lite for about 5 months (how time flew)... At first, I only got Castlevania Portrait of Ruin which i bought with the system. I also play PC games. So, the only time i play on DS was mostly during trips to/back from work while the rest of the free hrs of gaming spent at home were on PC games (more like, game, UFO: Afterlight)
As I got more games, I began to play on the DS more. Up until now, I hadn't played any PC games for a month. So, DS is currently where I spent all my gaming time atm.
Last 2 weeks or so, all of the sudden, my sis' family got themselves a DS lite with brain age game. I often see them glued to the DS instead of the Wii or Gamecube. My nephews, 3 and 6 yrs old boys. They got around 10 or so gamecube games on 2nd floor and 5 or so Wii games on the ground floor (with big screen TV).
Normally, the games were for the kids only. My sis and bro-in-law don't really play them. But now, they do, on the DS. The kids still plays on console when their parents hog the DS.
I would say, the DS got the most attention, then the Gamecube (sonic and mario), then the Wii (Wii sports). Wii doesn't get as much attention probably due to the TV being used more often and the small TV for gamecube only used for gaming for the kids.
I never really got into Brain Age and don't understand why they love it so much but the DS sure is getting a lot of attention. Perhaps, that's why the everyone and his/her grandma owns a DS? :)