I've been playing a couple of boardgames with my kids lately.
The Dungeons & Dragons Computer Labyrinth Game [http://www.boardgamegeek.com/boardgame/4746/dungeons-dragons-computer-labyrinth-game] and Dungeon Dice [http://www.boardgamegeek.com/boardgame/1555/dungeon-dice].
The D&D game is pretty fun, though it can sometimes be a bit tough to figure out exactly where the dragon is so as not to be munched by it. And it can be played single-player (though I have yet to play it solo.) Dungeon Dice is pretty simple, enough so that my 4-year-old son can grasp the gameplay enough to have fun with my 10-year-old daughter and I (the D&D game is a bit much for him but it looks too cool with the figures and all the wall pieces) so he always has his nose in it when we play.
I picked both up on eBay. Dungeon Dice goes for pretty cheap but the D&D game can get pricey and it's tough to find one complete (4 figures, 50 wall pieces, 3 green markers, instruction booklet, battery door, pull-out tray...and make sure it actually works.) I got my D&D game for $35-$40 complete in NM box, was pretty stoked; more so now that my daughter wants to actually play it with her nerdy dad.
EDIT: One game I've been itching to play is Tannhauser [http://www.boardgamegeek.com/boardgame/25261/tannhauser]. The art is really cool and there are so many cool bits to it, a very visually-appealing game. Kinda expensive new (I think I saw it for $80 at my FLGS) which is why I haven't picked it up (plus, I need to have friends around to actually play it.) Someday...