My boyfriend is very unlike me which is why I like him so much. I'm on the quieter side and he's extremely outgoing. I'm more emotional and reflective whereas he's pretty much the opposite.
It works in some ways and doesn't in others.

the last guy i dated was my opposite. he was my coworker's roommate and asked me out for a drink right after i found out how old he was, so i declined. but we happened to both show up at a friend's gathering one night and ended up talking in the corner for 3 hours oblivious to everyone else. i discovered that he was a physics major and was actually very sharp and intelligent.
after our second night out i found out he was an officer in a fraternity, he drove a bmw with a retarded lcd screen that came out of the dash, had a framed picture of himself in front of his car in his living room, owned a roomba and used it almost every day, and right before we stopped seeing each other he got a pete wentz fauxhawk. and sadly, the only reason we stopped seeing each other is because i didn't have time for him. or as he put it, i wouldn't make time for him.

I think it depends what you mean by oppisite. It seems fine to have oppisite interests but not oppisite personality traits, if you get what I mean?
This isn't actually a well thought out hypothesis. My bf and his mates we're talking about this the other night. He was telling them that we're oppisites but they disagreed saying we were both stubborn and obsessive (just about different things). Thinking about it, they were right.

my bf and i have completely opposite personalities.

he's quiet and shy and very anxious about everything. i'm loud and outgoing and have a who cares attitude. he's very nice and polite and sweet to everyone, and i'm more abrasive. nothing about our personalities is similar.

Well, there is such thing as a clash of personalities, especially among people with self-identity issues (and at the end of the day, don't we all have issues with self-identity?). I would almost say that the opposite holds more truth, that a common interest brings people together but differing personality traits would prevent them from becoming boring to one another.

I think a balance is necessary. Different enough to be interesting to each other but similar enough to get along.