This is a loaded question. Meaning, it is very hard to give a set amount, like this CPU/memory/HD package can support this.... Etc etc.

Your uplink and bandwidth matters how many concurrent users can be using a single box. Then, what is the box itself doing? MySql, video conversion, mail, streaming?

You will find a single box will tap rather quickly when using streaming, unless it is a monster. A vps will definitely tap out quickly, and probably get you banned.

Also, which web server? Using a proxy for static files? Apache for the back end? Php-fpm? All optimized? Memcache? Etc etc

Everything matters.