Do USB keyboards have a limit on how many keys can be pressed simultaneously, like PS/2 keyboards?

It's a matter of key switches, not keyboard connection.

My PS/2 keyboard uses mechanical switches and can handle all keypresses at the same time.

My Microsoft Office keyboard had a limit, I think two was the maximum before the computer beeped.

I don't think its to do with the switches but rather the keyboard controller and its buffers.
Could be both...

Anyhow theres an application called keyscan which can test how many keys in total you can register.
My slim Apple keyboard manages 5

Two? So not even CTRL+ALT+DEL worked?

That worked. However pressing any other 3 buttons resulted in a bleep from the PC.
Maybe the KB controller registers it as one keystroke?

Looking around on the net apparently the Omnikey 101 is keyboard god...11 keystrokes apparently.

I tested the notebook keyboard with that tool you mentioned and while it only accepts only 3 keys at a time, it seems that CTRL, ALT, Shift, Caps Lock and Num Lock can be all pressed simulataneously without problems (in addition to those 3 keys I mentioned). Maybe that is why CTRL+ALT+DEL works.

http://en.wikipedia.org/wiki/Rollover_(key)

I've tried and tried but couldn't dig it up, but there used to be a keyboard testing program at the DJGPP sites.

With a mechanical keyboard it really did show all keys being pressed at the same time, without any beeping.