Are there any great, lightweight MySQL connection classes out there for PHP that anyone recommends?

I have written my own, and I do think it is pretty good but this seems like the sort of thing that many programmers better than me must have perfected long ago.

I'm interested in finding something that I can slot in generically and use as I need it with as little hassle as possible.

Some generic functions to support querying, connecting to multiple MySQL databases within the one application would also be a plus.

Originally asked by: Evernoob on Stack Overflow