Each MySQL connection actually uses several meg of ram for various buffers, and takes a while to set up, which is why MySQL is limited to 100 concurrent open connections by default. You can up that limit, but it's better to spend your time trying to limit concurrent connections, via various methods.
Beware of raising the connection limit too high, as you can run out of memory (which, I believe, crashes mysql), or you may push important things out of memory. e.g. MySQL's performance is highly dependent on the OS automatically caching the data it reads from disk in memory; if you set your connection limit too high, you'll be contending for memory with the cache.
If you don't up your connection limit, you'll run out of connections long before your run out of sockets/file handles/etc. If you do increase your connection limit, you'll run out of RAM long before you run out of sockets/file handles/etc.
Regarding limiting concurrent connections:
- Use a connection pooling solution. You're right, there isn't one built in to PHP, but there are plenty of standalone ones out there to choose from. This saves expensive connection setup/tear down time.
- Only open database connections when you absolutely need them. In my current project, we automatically open a database connection when the first query is issued, and not a moment before; we also release the connection after we've done all our database work, but before the page's HTML is actually generated. The shorter the period of time you hold connections open, the fewer connections will be open simultaneously.
- Cache what you can in a lighter-weight solution like memcached. My current project temporarily caches pages displayed to anonymous users (since every anonymous user gets the same HTML, in the end -- why bother running the same database queries all over again a few scant milliseconds later?), meaning no database connection is necessary at all. This is especially useful for bursts of anonymous traffic, like a front-page digg.