https://www.youmagine.com/
Ultimaker-centric. Lots of Ultimaker replacement and upgrade parts. Intends to start an online design tool, but I don’t see it yet.
and https://www.youmagine.com/collections Some potentially interesting content. Not as deep a collection as thingiverse.
http://www.yeggi.com/
3D search engine, which incorporates data from other 3D object libraries.
http://www.thingiverse.com/
This seems to be the most popular, most commonly reference library of freely available 3D objects.
https://3dwarehouse.sketchup.com/
Mostly not 3D objects, but all 3D sketches. Mostly scenes, buildings, cars, etc, but not intended for 3D printing.
http://www.openscad.org/gallery.html
A very small gallery.
https://gumroad.com/library
Not exclusively a 3D object library.
https://www.cgtrader.com/
Nice library of components, e.g. gears.
See also: