Fancy things: Kollwitzplatz on Saturdays has some nice trinkets and gifts and things, as well as some decent food.
Art and craft: Am Zeughaus on Saturdays and Sundays.
Junk: Mauerpark fleamarket on Sundays is the biggest and probably the most interesting flea market. Lots of cool junk, bikes, furniture and even pianos. There are also a few stalls selling things like original screen-printed t-shirts and jewellery, if you can find them amongst the junk.
Junk: Boxhagener Platz on Sundays is much smaller than Mauerpark and has less variety, but is worth a look if you're in the area.
Fruit/veg/meat/fish/bakery: Boxhagener Platz on Saturdays. Stalls are mostly closing by around 3pm in winter, 4pm in summer.
Fruit/veg/fabric: Maybachufer (near Kotbusser Damm) on Tuesdays and Fridays. Lots of cheap fabric.