I'm curious about what you mean by 'most amount of people you have had on your site at one time'. This can mean a few different things...
1) For monitoring applications like Chartbeat, IIRC they count a user as concurrent if they are on the site anytime within the past 30 seconds.
2) I've seen real-time monitoring systems count a concurrent user as any visitor in the last 5 seconds.
3) Lastly, the only real raw numbers that I've seen are the traffic hits through an F5 load balancer to a set of backend servers, and that is the only number that will give you an unbiased # hits per second in real-time. Unfortunately, this amounts to requests (HTML) to the server and may not be a 1:1 ratio with users.
So in terms of what I've seen, it depends on the type of calls and the application. For the EA forums (forums.ea.com) which I was in charge of up until March 2013...
For #1, forums would regularly reach 15,000 on the launch of a new game. We would sustain that for ~12 hours [1]. On just an average normal non-event day, it pushes 3000 concurrents.
For #2, I've seen something north of 3000 for EA forums.
For #3, the F5 would report peaks of 200 requests per second.
When I built the Campus Wide Login (http://www.cwl.ubc.ca) SSO auth system for UBC about 11 years ago (still in use today) we would have almost 50-75% of the full campus using it at once, which is about 30k concurrents (unfortunately I didn't have access to the numbers over the F5 LB). However, most of these calls were for the HTML which then went through an SOA (XML-RPC, ugh) architecture, so I'm sure the req/s was much higher on the XML-RPC backend.
[1] this is a feat in itself because most of the forum data is not cached because the business wanted the data in real-time, so the read databases would receive a lot of traffic when the web servers spiked.
Edit: formatting
