The most popular sodas — including this extensive list from Coca-Cola and all carbonated sodas from Pepsi Co. — are considered gluten-free to 20 parts per million.
Fruit juices also are gluten-free, providing they're made with 100% real fruit. Therefore, orange juices and other citrus juices you find in the dairy section should be safe (although some sensitive people report reacting to some orange juices).
Fruit drinks, on the other hand, aren't made completely with fruit, and may contain some gluten ingredients — you'll need to check with the manufacturer before purchasing to be certain whether they're safe or not.
Unflavored coffees and teas are gluten-free, but some flavored coffees and teas (especially herbal teas) contain gluten — check ingredients lists or steer clear. Some blended coffee drinks are safe and some are not, so again, you'll need to check the ingredients. When I'm at a coffee house, I order a latté or a cappuccino, both of which contain only milk and espresso.
Gluten-Free Alcoholic Beverages
If you're shopping for beer, you need to stick with gluten-free beer; other beers contain barley, which is a gluten grain and therefore unsafe on a gluten-free diet. Wine should be safe (unless you're particularly sensitive); here's some more information on Is Wine Gluten-Free?.
When it comes to gluten-free alcohol, there's some debate over whether alcoholic beverages derived from gluten grains, such as whiskey and gin, are safe or not. I personally can't drink them without a major reaction, and I'm not alone — plenty of people report reactions to gluten grain alcohol.
One more thing: you'll need to make sure any mixers you use for your drinks are gluten-free ... some aren't.