At least 30 most likely more

I haven't been keeping count, but so far it's more than I died in my first playthrough of vanilla Fo3 (not counting times I was just screwing around.)
Just an hour ago I stumbled into a cavern full of Deathclaws... That didn't end too well.

My companions have died a lot more than me though. I'd say it's a 70/30 split on the reloading saves XD I gave up on ED-E early, and am starting to feel the same way about Rex, he's even worse at getting himself into trouble