These are all great suggestions. Thank you very much, everyone! I was originally asking because I work with a lot of kids and they know I like games. I think for now, Chrono Trigger is a good one to suggest since it's also on the DS and lots of kids have one.
I'm still thinking about which game I'd like my own daughter to play first but that is years from now. Children shouldn't watch TV until their 2, by the way. There is some useful information from professional doctors for all the parents out there. ^_^
Chrono Trigger is a good choice, however depending how old the child is...
You might want to make sure they save Lucca's mother leg's from being crushed and living with the guilt that they couldn't save her.
That was a little nerve-racking when I first played it when I was a kid.