For myself, I've found it's not the razor, per se... but the hair growing back through the skin. The hair growing back through creates tiny little "bubbles" in about 1:4 follicles, and then if I shave, I'm slicing the tops of the 'bubbles' off. Which hurts. And then, of course, they're all red.
To completely nix the itch/burn... I just use a poofy-thingmy (the plastic bathpoofs) with some neutragena acne bodywash, and only shave every other day. I scrub my legs every day (before shaving on shave days), but the day in between I make sure to be really thorough. It exfoliates the little bubbles off and allows the tiny hairs to poke through, and the body wash keeps any infection from happening. Next day, I scrub again, and then shave.
Since I started no more oweeeeee! shaving, and no more pseudo-burn.
((I use a Fusion 4 blade razor, btw. Goregous razor that just sliiiiiiides and deals with my combo of coarse/fine hair like a dream. Not the electric one, just the normal one))
For my bikini area which gets REAL razor burn, I just apply Secret Solid Unscented deodorant after shaving, and ANY time I feel any friction or heat. Voila. Magic.