Vodka made from non-gluten sources, such as potato vodka or grape vodka, is usually gluten-free. However, there's some controversy over whether vodka made from a gluten grain source is gluten-free.
Most experts on celiac disease believe that distillation removes enough of the harmful gluten proteins to render alcohol made from gluten grains gluten-free. In fact, the National Institutes of Health advises that distilled alcoholic beverages are safe to drink, even if they're made from gluten sources.
However, many of us who are very sensitive to gluten cross-contamination (me included) get truly nasty gluten symptoms from any form of alcohol that started its life as gluten grains ... and that includes vodka made from wheat or rye. In fact, the Celiac Sprue Association recommends against consuming gluten-based vodkas.
Fortunately, there are plenty of vodkas on the market that are not wheat-based (although some are made in facilities that also distill gluten grains).
Potato vodka is quite common (especially in imports from northern Europe), and one common vodka distillery (Smirnoff) makes its vodka from corn. Other, smaller companies make well-rated vodkas from grapes. For a complete, extensive list of gluten-free vodkas (including potential cross-contamination issues and some other shopping hints), check out the Gluten-Free Vodka List.