The question of the effect of applying for lots of credit cards on FlyerTalkers' credit ratings has recently been discussed at length in another thread entitled How many affilitated cards do you have? in MileBuzz. (sorry, I can't figure out how to post the link).
After reviewing that thread I hold to my original opinion, which is that while applying for, and not getting, credit cards hurts your credit score, applying and getting the cards has very little effect. When an account is opened the inquiry is supposed to be automatically merged into the newly opened account (when first use is reported to the bureau) and so the inquiry effectively disappears and has no effect on your credit score.
Gather your miles while ye may!