Danc at Lost Garden has a blast from the past up, in the form of a snip from a talk given by Dani Bunten Berry on good design elements for multiplayer games (all the way back in 1997). It's quite a list, but just goes to show that a lot of good design elements are pretty timeless.
"Zero sum" is bad. Games where I win and you lose are bad. Worse still is "I win and all the rest of you lose". Notwithstanding the current cultural obsession with endzone strutting by winners, losers do not enjoy themselves and if you can help take the sting out of it, you should. Alliances, cooperative play, ranked "winners" rather than "A winner" with a bunch of losers are all options. Pacing needs variety. Slow periods should follow intense ones and forced "time-outs" can offer opportunities to socialize, catch your breath and anticipate things to come. Remember, the players no longer have a "pause key" as they did in a solo-game. Strategies need "wiggle room". People have different personal styles and when playing against each other it's great to let them "do it their own way" rather than a single approach that all must follow. If possible you should balance the game such that a strategic planner for instance might not always beat the joystick jockey or the detailed tactical type. A game that allows for diverse people to play diverse ways is always best.
There's much, much more, but it is interesting to see what we're still talking about in regards to multiplayer game design. We'll find out shortly what gems this year's GDC will produce.
GDC: Social lessons of years past [Lost Garden]