I'm a big fan of the Columbia Heights Community Marketplace, which aside from produce, meat, cheese and dairy also has crafts and other services. It's pretty great. It's on Saturday from 9am-1pm at the Columbia Heights Civic Plaza, the triangle where 14th, Kenyon and Irving meet.
Mt. Pleasant's market is a bit smaller, but still with a nice selection and a good, neighborhood-y vibe. Random neighborhood folks will play music there sometimes and it's great to go shopping and then grab a coffee and pastry across the street at Heller's Bakery. They're also open every Saturday from 9am-1pm at Lamont Park, where Lamont hits Mt. Pleasant Street.
I haven't been to the Petworth Community Market, but they have the distinction of being open on Friday afternoons, from 4pm to 8pm on 9th between Georgia and Upshur.
14th and U is one of the older markets around, and as such has a pretty big vendor presence. They're also open Saturdays from 9am-1pm.
So go! Which is your favorite?