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Some good individual suggestions, but here's my own take on it:
There's simply too much stuff going on, on a day-to-day and week-to-week basis, to ever possibly list them all in an Internet message board forum. Your best bet is to seek out some local pubs that have listings of what's going on and when. Some of the best include the City Paper, the Current newspapers, Washington Post's Going Out Guide, the InTowner and (yes) the Onion. Most of these pubs provide lists of things to do by subject--museums, galleries, performances, readings, festivals, etc.
Another great source of fun and unique events throughout the city is the DC International Club. It's free to sign up, and they put on some fantastic events throughout the year that attract really interesting crowds.