Granted, libraries are beneficial and some of the functionality they offer is down right invaluable (see: YUI Event Utility). But I’m of the opinion that any programmer that’s serious about their work should at one point or another have at least attempted to write the very same code found in those libraries themselves.
Think about it, what benefit is it to you as a programmer, to download a library, plug it in, and watch it do magical things for you? It might make your site look cool, but you’d benefit very little if anything at all as a programmer. You’d get much more out of the painful experience of knocking your head against the wall and trying to figure out how to do things for yourself. It’s a foregone conclusion that the best way to learn something is to get involved. Thus, to learn to be a programmer, you need to program!
Realistically though, time and budget constraints don’t always allow for the writing of programs from scratch. But that isn’t the point. The key is to take the time (your own time if need be) and learn the language for yourself. Otherwise, all you’re doing is glorified copy and pasting.