I like to do other stuff while I play my Nintendo DS -- watch TV, listen to podcasts, listen to my girlfriend's nagging, etc. I find games that don't require much attention, without time limits to be best for this. My previous best is Puzzle Quest, which was perfect for this sort of thing. Also pretty decent was Picross. Now that I've beaten both of these games, I've resorted back to solitaire on my phone.
I'm looking to pick up a new game, and I was thinking about either Civilization: Revolution or Final Fantasy 4. I've never played a Civ game or a FF game in my life, so I don't know much about them. Can you play them casually while doing other stuff and not really paying attention?
What other games fit these criteria?