As noted above there are many factors that affect your score, and applications are actually fairly low in terms of the hit you take on your score.

For the past 5 years I have been getting alerts from equifax (which uses real FICO) every time my score changes. From what I've observed the biggest hits have come from increasing my utilization on an individual card, this can knock the score anywhere from 20-40 points, particularly if more than one card goes up at the same time. Note, it doesn't matter whether I carry the balance, I get the hit just the same if I charge $5k on $10k card or do a 0% balance transfer. The score usually goes back up when I pay off the card, but not always by the same amount. Applications seem to have little effect though paradoxically I've seen scores rise when a new card is reported (lower utilization I guess). The other major hits come when you close an old account - this seems to unfairly penalize consumers when banks change the terms, i.e. new annual fees, etc. But this effect is also reduced as you get older and your other accounts age.

Over the past 3 years we've bought 1 car (.9%) and closed 2 home mortgages (the latest at 4.25%/30year fixed) so I have never felt it prudent to play the app-o-rama game. We generally apply for 1 new mileage-bonus card per person each year, and don't seem to have any problems.

However if your score is within 20 points of the cutoff - 760 and 720 seem to be key threshholds - I would not roll the dice for a few miles if you have a major mortgage in the works. the difference between .25% on the life of a loan will cost you far more in real cash than the value of your FF bonus miles, even if you refi later you'll pay thousands in costs. Better to wait - there is always another deal around the corner.

Now of course if you don't need a mortgage, your credit score is 780+, and you don't plan to jack your utilization with high balances (i.e. for a 0% offer) then by all means apply as you wish. But not too many people fall into that category.