It's easier to try and stick with one airline if possible.
In some cases, airlines have a partnership, which allows you to fly on a flight operated by one airline, but earn frequent flier miles on another.
There are 3 big "super alliances" that have many domestic and foreign carriers as part of the alliance:
Skyteam: Aeroméxico, Air France, Alitalia, Continental Airlines, CSA Czech, Delta Air Lines, KLM Royal Dutch Airlines, Korean Air, Northwest Airlines
OneWorld: Aer Lingus, American Airlines, British Airways, Cathay Pacific, FinnAir, Iberia, Lan, Quantas
Star Alliance: Air Canada, Air New Zealand, ANA, Asiana Airlines, Austrian, BMI, LOT Polish Airlines, Lufthansa, Scandanavian Airlines, Singapore Airlines, Spanair, Thai, United, US Airways, Varig
I'd second Safetymom's recommendation of heading over to FlyerTalk for more information than you'll ever need about airline frequent flier programs.
I'd recommend trying to stick with one airline if possible. That way, you'll earn reward flights faster (takes about 25,000 miles earned for a free domestic round trip ticket). If you're doing a LOT of travelling (more than 25,000 miles in a year), you would want to look into the benefits of being a high-mileage traveller, as different airlines would offer different perks (more frequent upgrades to first class, etc), and you may want to either try to focus your flights on one carrier, or try to spread out enough to maintain "elite level" status on multiple carriers.