The Pokemon games are masterful creations. Primary school children can complete the games without seeing the complexity in them. Older kids and adults can get deeper into the games and pursue other objectives that are available.
I have ignored quite a few of the gameplay possibilities but have still sunk well over 300 hours into the games. That is awesome value for money.
The games routinely get rubbished by "serious gamers" who seem to just like shooting other people with photo-realistic combat games. But as you can see from the reviews on http://www.gamefaqs.com/portable/ds/review/946308.html many people disagree. The other thing I like about the games is that they are not real-time. I am getting too old to enjoy games that require fast reflexes.
Depending on the kind of anime you are into, you might like Pokemon. It comes from the same wacky Japanese pop culture.