I think traditionally, something like Tomcat used to have perhaps 30 threads? Especially with todays Ajax-driven web sites, it is very easy to exhaust them.
I can only point to a stupid app of mine, which triggered Twitter searches for a list of search results via Ajax (so one page of search results would trigger, say, 10 search reguests to Twitter via Ajax, proxied through the server). Since that app was written for a competition and non-commercial, I hosted it on the free Heroku plan (it was a Rails app). That is how I found out that apparently that Heroku plan has only one process, and Rails doesn't use threads. So not only would the search requests to Twitter only be handled sequentially, while those threads were running, no other visitors would get to use the site (the 10 Ajax requests would already use up up to 10 threads, and I had only one).
Just a stupid example - with event based request handling, it would not have been an issue because the search requests to Twitter would not have blocked everything else.
But a request to twitter blocking everything else would be an issue, right?
Aside: haproxy, configured cleverly, can deal with limiting the number of concurrent connections permitted to your app on a URL basis (or just about any other part of the request you can deconstruct) to allow your app to not get hung up on slow queries and keep fast queries going where you want them.
I can only point to a stupid app of mine, which triggered Twitter searches for a list of search results via Ajax (so one page of search results would trigger, say, 10 search reguests to Twitter via Ajax, proxied through the server). Since that app was written for a competition and non-commercial, I hosted it on the free Heroku plan (it was a Rails app). That is how I found out that apparently that Heroku plan has only one process, and Rails doesn't use threads. So not only would the search requests to Twitter only be handled sequentially, while those threads were running, no other visitors would get to use the site (the 10 Ajax requests would already use up up to 10 threads, and I had only one).
Just a stupid example - with event based request handling, it would not have been an issue because the search requests to Twitter would not have blocked everything else.