If I flew only a few times a year, they would be lo-o-o-o-o-o-o-ng flights so that I could still be a Premier.

I would still concentrate them in one program, either United's or Alaska's, to earn miles and the shot at an upgrade every few years. I would use one of those airlines because they have the best service to my home airport.

If (to extend your question one step) airlines had no FF or mileage-based programs, then domestically I would fly nonstops as much as possible, on any airline except Southwest (hear, hear, mdtony). For the occasional international flight I would use Virgin or BA to the UK and spread trips to other places around lots of airlines, for the sake of variety.