My company blocks ALL external mail (as well as Facebook and such). it’s a very big company, though, so the resources exist to selectively filter things (for example, Gmail is blocked, but Google isn’t).
Personally, I’ve always thought of web-based email as a nice convenience, but not a real show stopper. I use a fat client that accesses POP and SMTP servers – and every POP server is pretty much like any other – brand is not that important. Now, if my company doidn’t block web mail, I might sing a different tune.