Alaska Airlines will let coach ticketed passengers upgrade to first class for $50 at the gate, on a first come first served basis.
Does anybody know if any of the other big airlines do this too?
Delta does it also, based on availbility.
Yup, I can confirm that Delta does it at some airports.
Not that I’ve flown Coach since…October 2001 on Delta (out of about 50 flights). 
I’ve had a free upgrade on British Airways; once this was just because I asked nicely at the check-in (and I was smartly dressed), the other time it was because they asked me if I would mind taking a flight an hour later for £80 cash (It was a business flight and I was in no particular hurry, so I said yes, but in the end they didn’t need me to, but they upgraded me as a thank-you)