The only true phobia I have, which I have learned to get over, is bees and bee-like things (hornets, wasps, etc.). If I was too close to one I could feel the fight-or-flight start creeping in. My wife is a gardener so I have learned to appreciate them and overcome most of it, but occasionally one will fly too close and I'll sprint off like a maniac.
I have only mild twinges in certain heights- like climbing a tall ladder. Nothing that stops me, I just feel it there and control it. No problem with planes- in fact, I've flown some myself. Same with little twinges of claustrophobia- if I crawl down into a small man-sized hole I can feel it lurking at the edges, but I control it.
Just invoke the Litany Against Fear:
I have a bee phobia too but really admire bee-keepers. Russell Brand has 60,000 bees btw.