I always prefer third party libraries "when possible", and so should everyone else who isn't just playing around to explore new programming techniques. The problem is defining "possible" for your particular circumstances.
In my case, I need a third-party library to at least fit the following criteria:
1. open source, so I can adopt and maintain or modify it if needed, and be more likely to get responsive help from the "official" maintainer
2. copyfree license or public domain, so I never have to worry about licensing entanglements caused by non-copyfree licenses (this means no GPL, no LGPL, no Apache License, no proprietary, and so on)
3. well-designed, obviously -- by someone who knows something about the particular field in which the library applies (especially important for stuff like security libraries; authentication, cryptography, et cetera)
4. clean code, so I can understand its internals, and some combination of good API design and documentation so I can understand how to use it
5. provides what I need, without providing too much more than what I need so that needless complexity will not introduce problems I would like to avoid
Most of the complaints I see in this discussion about problems using third party libraries are about not being able to keep their functionality up to date and get bugs fixed in a timely manner -- problems which do not apply to open source libraries any more than they apply to libraries you write yourself. One or two complaints are about not being able to make changes to third party libraries as easily as you can do so with libraries you write yourself, which is silly, as long as you adhere to the fourth requirement in my list above; even your own source code essentially becomes foreign source after a few months of doing something else, after all.
When there isn't something that fits all my requirements, I end up having to write my own, of course. That's the point at which the "when possible" fails.
edit: Y'know, the entire history of human progress is about how innovative people build on the work of those who came before them. We all use someone else's work in everything we do. I find it frankly shocking that the idea of using third party libraries, when available libraries meet our needs, is at all controversial.