Edit here at the beginning. It took 20 minutes to do this....so when I pushed the preview button, I saw that back in 2002-2004 there were three threads on this subject, including two from the same person!
US State With The Most Commercial Jetports (by Zrs70 Dec 18 2002 in Civil Aviation)
What State Has The Most Commercial Airports? (by Ssides Dec 9 2003 in Civil Aviation)
Which State Has The Most Commercial Airports? (by Ssides Mar 3 2004 in Civil Aviation)
So, I'll make a little change.
What state has the most airports with MAINLINE service?
WOW ...just realized Florida has 19 with mainline service.
All of those have mainline.
I don't think APF has any service currently, so that just leaves MTH, but I don't think anyone is serving it currently.
Airports in Florida (besides the ones mentioned) that used to have service:
Vero Beach (VRB)
Titusville/Cocoa Beach (TIX)
So there are three states with a bigger population ....Texas, California & New York. Because of the uniqueness of Alaska, they have to be considered as well.