Amber is the most distinctive purchase in Riga. Latvia sits on the Baltic amber coast and the city has dozens of amber shops, ranging from high-quality goldsmiths to tourist-trap stalls. For the former, look around Alberta iela and Valdemāra iela rather than in the Old Town. Prices vary enormously; natural amber with inclusions (insects or plant matter trapped inside) commands a premium.
The Central Market is the place for food to take home — smoked fish, jars of honey, pickled mushrooms, rye bread, and Black Balsam liqueur. The dairy hall has excellent local cheeses.
Berga bazārs, a renovated 19th-century commercial courtyard complex on Elizabetes iela, has good independent shops and is a more pleasant alternative to the Old Town souvenir strip.
Latvian linen — tablecloths, towels, and clothing — is high quality and not inexpensive, but it's a genuine product of local craft tradition.