There were several fairly well known libraries a couple of years ago, but as far as I can tell, jQuery won that battle decisively. It has almost 100% penetration in the projects I'm familiar with that use a general purpose JS library, and it seems to be the default for articles and blog posts I find on-line these days too.
Part of that success came from the ecosystem reaching critical mass. Many people know jQuery. Many plug-ins are available for jQuery. And the vast installed base usually means quick bug fixes even for recent browser compatibility problems.
If there is something out there that is better by a wide enough margin to justify giving up that established ecosystem, I'd love to hear about it. The ecosystem has plenty of imperfections, but I haven't come across anything yet that seems nearly comprehensive enough to displace the incumbent here.