Keep in mind, the Wii isn’t all kids’ games. I own one, and we have Resident Evil 4 which has lots of slaughtering of very realistic zombies in it. My husband and I haven’t owned a Nintendo system before (previous history includes Atari 2600, Sega Genesis, and Playstation 1 and 2), but we still enjoy it even without the history of Mario/Zelda/Rayman/Mega Man fandom. We also don’t have kids.
The majority of the games are skewed towards kids, but adults should enjoy most as well. The Lego series of games (Star Wars, Batman, to a lesser extent Indiana Jones) have all gotten very good reviews from what I’ve seen, and I plan to buy Star Wars soon.
I own Rayman’s Raving Rabbids which is a cute game full of lots of cartoony violence. This might be more fun played with a friend/sibling/parent as you get to laugh at what the other person is facing, cheer them on, etc. Lots of super-short “mini-games” to try out. Stuff like wiggling the controllers as fast as you can to deliver an exploding present, which does the cartoon ‘sooty face’ result to the Rabbid who receives it, or flinging a cow like you’re in the Olympic hammer toss competition. I got my copy at Target recently, for $20. There’s a sequel out which is around $40, so try the cheap one first.
Get WiiPlay packaged with a second controller. That way you can have two controllers, and you get another series of mini games for a decent price.
Some games require a “nunchuck” - I forget if we bought ours separate or if it came with the system. Check the backs of games you buy to see if it shows a little crescent-shaped controller in addition to the stick-shaped regular controller.
Check the games forum - I know there was a Wii games thread there in just the last day or so. You might find good recommendations there.