Which airline you select can depend on your home location. Example: folks in Dallas might go for the Citibank Mastercard that earns American Airlines points due to American having a major hub there. People in Houston might go for Continental's affinity card with Chase or American Express card (Green, Gold, or Platinum one).
You should consider which airline suits you based also on where you might want to go to determine who services that destination city. More flights for that airlines means more free ticket availability.
As mentioned, several credit card issuers are offering signup bonuses. If you do some research on this forum, you'll quickly begin to understand all of the acronyms.
Some folks limit themselves to one card if they don't use their cards too often and still want to earn enough to eventually get a free tickets. Those who can charge more might opt for two or more cards to gain flexibility. Most airlines offer partnerships with other airlines. Consider researching this.