The Tourist Office has useful Buy Local map-guides to Maastricht's independent shops. Stokstraat and Rechtstraat are interesting for casual browsing with a scattering of minigalleries and interior-design boutiques. The streets off Grote Straat have more mainstream stores and there are two appealing central malls, Entre Deux and Mosae Forum. On Thursday evenings most shops open late (till 9pm).
The Markt is the scene of several markets, general on Wednesdays: fish on Fridays and brocante (ie used everything) on Saturdays and Sundays. There's also a Thursday afternoon organic market.