I carry two spares. Why? Dunno, maybe I'm just paranoid! One reason is that I got my matching second spare tire for like $10 brand new from someone getting rid of stuff in a shop.
When I was 17 I traversed southern Utah in my FJ40 with some friends for about 2+ weeks. There was a gal with us who was driving a Bronco II that had two tire blow outs. We used someone else's spare tire on it. Personally, I've never had two flats, but I have seen it happen on long treks. I honestly don't remember the brand tire; I know I had BFG ATs at the time and at least that trip didn't run flat.
I always carry spares for anything that reasonably wears and would reasonably prevent me from limping home. 2 starters, 2 batteries, and 2 spare tires. I need a spare used alternator ;-)