There are a couple reasons I can think of to use a library:

* The code is the best in the world and would take anyone years to compete with its speed. Libraries like gmp, fftw etc come to mind.

* The API is good. A good API extends the language in a way that makes your code better and more enjoyable to write.

I usually try to avoid dependencies where possible because it will always make life easier later on. Introducing a dependency for a single function should be a sackable offence imo. At that point you're just too lazy or incompetent to do your job.