Let's throw some numbers around:
- 1,000 at a time should be no problem at all, in general.
- 10,000 at a time will work but you have to know your entire setup intimately and never block any of the CPU's waiting for any I/O, as well as not be limited by your bandwidth. (assuming 10KB per http request and response @10,000 requests per second, that's 97 MB per second)
The rest of this answer is just some discussion to just point you in some direction
I've thought of this question a few times, and because you are looking for ball park figures then this might help you:
Looking at front end dedicated servers that handle a specific task (but talk to other services to do work for them, like the google search infrastructure which would call on many other machines to get pieces of information), then your front end machines that handle the actual client sockets should be able to handle about 15,000 users concurrently (ballpark, assuming binary protocol) because if you look at how many players play per server on WOW, depending on the strength of the machine, they have from 6-30,000 users per "world" - which I assume is one machine supported by other services at the back. I can't find the page now that lists servers and players per server. This isn't a web site though, but you are looking for ballpark information and this might lead you to the right place.
Have a look at wikipedia's server stats if you are interested in some architecture numbers - http://stats.wikimedia.org they show every detail you might be interested in regarding http requests.
Looking at IIS stats, take this site for example, stackoverflow.com - they were doing 16 million hits per month on 2 web machines and I'm sure more than 1000 people must have been on it at a time. There's an article on HighScalability.com about stackoverflow's servers.