It all depends on your situation and goals.
Of course, we'd all love to use reliable mature pre-made libraries with the exact feature set and API that suits us. Why wouldn't you? Saves time and money and can bring in expertise, because we can't all be the best at everything.
But I just hate trying to debug someone else's library. You lose the time benefit and I guess the fact that you're debugging shows you didn't get any maturity/reliability either. And as someone else says, the more bloat you add the worse your app gets on a number of fronts.
So you've got to balance up what's important for each development and the quality of the libraries on offer.
I'm prefer my own stuff in many situations. I'm even wary of jQuery, for instance, because of bugs or workability problems that I've encountered, even though many web sites are built by default from jQuery, but I answered the poll as "use pre-made whenever possible", because if possible that will save time and should bring in maturity.
I don't get what @jarzola said: never use library for core - not good design? Just don't get that comment. Every library is important, core or not, and needs to be reliable and efficient, all of them, all of the time. Either you've got a library that's fit for purpose (so use it) or you haven't (so don't).
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