If you like yahtzee, there are plenty of versions in the store with hotseat multiplayer for 4 players. As the developer of one of them, I've looked around a lot and most of them look pretty good if that's what you're after (sharing one device). For online multiplayer, there's only three so far it seems, and only my game supports 4 players over Game Center (that's actually the reason I made it, since I love yahtzee and I wanted to play online). For hotseat games, most of them are decent or good, but Yahtzee Adventures obviously has a big following and is pretty good (except the lack of Retina graphics and online play) –*I've played it quite a lot. For a free game, Dice Fight seems pretty decent too. (My game is called Yacht Dice Games, you're interested.)
As for other games, I think Carcassonne is possibly the best digital board game ever made –*it is so lovingly crafted and polished to perfection that it's hard not to love it. Settlers of Catan is pretty good too. The iPad versions are of course even better.
For music games, I think Tap Tap Revolution is a lot of fun. It doesn't have real multiplayer, but by the nature of the game it's very easy to play it vs friends and family just by taking turns at the same songs.