Since I am a Retro-Sonic-fan I would suggest the Mega Drive (Genesis) ones
any day of the week, especially S&K, which was, for me, just the best one ever! ^^
I also like many of the Pokemon titles, but I suggest them only if you can play in an emulator
at above than average speeds, because the pace is kinda slow, and can be time consuming.
...

But there are some really nice games to play with other people.
I have a lot of fun when playing with friends or my family members.

Here are some multiplayer suggestions, to have fun at parties:

» Mario Kart 64 ... (if you can play with 4 people it is just crazy! )
» Super Smash Bros ... (just make sure not to put in your group the guy that always chooses Fox and kicks everyone out for some reason... )
» Mario Party 2 ... (use cheats to unlock the mini-games... because the board-type game takes too much time... )

Other games I played, for 2 players:

» Mystical Ninja II (N64, again. The cooperative mode is interesting to try. Just don't get frustrated if your partner keeps dying like me... )
» Pokemon Emerald (there was a GBA with a link mode... but is too much work to use codes to get pokemon with good moves in the boxes...)
(if you try it, though, get a piece of cardbox and make a few cuts in it so you can "insert" it in your screen to divide the windows. )
» Guilty Gear X2 (for PC... my brother made me play this one... ... I took never-ending beatings and the game totally destroys your gamepads! )
(very fast paced, but make sure you have a nice bond with the person you are up against or you can have... family issues... ^^')

I am sure there are more but my memory is getting rusty... (due to aging?)
(Gosh, I really have to get myself a job... )