Snag.svg - "jQuery for SVG"
Basic example of using Snap.svg:
Another thing we did in this video with Snap.svg is convert this CSS animation Pen over to Snap.svg, teaching us we can use Snap.svg to work with inline SVG already on the page. Adobe has collected a number of examples themselves.
Raphael - older library from the same creator as Snap.svg
GreenSock - "Ultra high-performance, professional-grade animation for the modern web." GreenSock is about animations on the web in general, but does support SVG. Here's a Pen where you can see how it works.