I think the ones from GoDaddy work fine in most browsers. Or no?

I had a bad experience where a customer trying to save a buck who got one of the $15 dollar startech certs offered by GoDaddy was screaming at me because their customers were getting errors and invalid certificate warnings. It worked fine in the his browser because the first time you visited the issuing website it offered to install the intermediate cert in your browser. It didn't work for J. Random Shopper and the merchant in question didn't find out about this problem until he was helping his sister purchase something from the store.

Thus my antipathy to GoDaddy; they made $15 bucks off that merchant, but I will recommend against them, because it's pretty sleazy to play that kind of game on people.

Actually, firefox 3 on xp is missing a godaddy cert line. Just install the certificate chain/bundle instead of the lone certificate and you'll be ok.

There are certain corner cases where this doesn't work (one that comes to mind is WPA enterprise certificate negotiation in Windows XP, completely unrelated to HTTPS).

If the requirement for "virtually all browsers" includes esoteric mobile stuff I'd be concerned about intermediate certificate authorities. If you're doing desktop applications/common mobile applications, these providers will have solutions for you.

That's not completely true. Almost all certifiate providers issue chain certificate (even VeriSign) because it is better security practice. You simply need to install the inetermediate certificate on the server and none of the visitors will receive errors.