One. I've opted out, so I shouldn't get any, but airlines seem to believe that buying a ticket from them establishes an "ongoing business relationship". Seems like a stretch to me, since it's not a credit relationship. Anyway, American Airlines sold me out to Citi bank. I didn't shred it yet, set it aside to call and try to opt out specifically with them. I've found that's hard to do. Both the airline and the bank say you have to make such a request to the other.
I was tempted to accept the card, actually. Most of these airline-branded cards offer non-expiring miles, or free baggage checking, etc. But where I live, you have to fly on different airlines depending on where you're going, and starting down that road I'd end up with more cards than I want to manage.
Edit: Oh yeah, I got the personal loan flyer addressed to "resident" from the predator down the street.
None, I'm opted out, however, I do receive Emails from Crap1 all the time for extremely low APR car loans, but yet they won't offer me any kind of CLI or Upgrade on my two CC's I have with them.