I get around 130,000 visitors per month to my forum at this time. I run my own server, a little Dell R200 with dual core and 2 gigs of volatile memory, and I colo it. I run cPanel and the memory is right on it's limits, so I need to add more soon. The server hardly ever sweats, and only really sweats for a few minutes when it occasionally comes under pressure from bots before the firewall locks them out automatically. The daily backup process is starting to push things over limit too... but generally, Apache usually reports less than three requests per second.
I have my own server because I have a very specific setup and need httpd.conf control etc.
I run Invision Power Board.