Several websites host 3D objects or models which can be downloaded, edited, and printed using 3D printers like the Makerbot Replicator. Here are a few of them:

Thingiverse: Thingiverse is one of the most popular repositories of 3D models and is directly associated with Makerbot Industries, the makers of the Makerbot 3D printers. The models on Thingiverse can be freely downloaded and printed, and many of them can be edited as well.

MyMiniFactory: This site provides a large selection of free and premium 3D models. All the objects on the site are guaranteed 3D printable.

GrabCAD: This site provides access to a large library of free 3D CAD models and also has a strong community of engineers, designers, manufacturers, and students.

Pinshape: This is another popular 3D model repository. It features both free and paid models and focuses on quality and printability.

Cults3D: This is a marketplace that connects designers and people who want to 3D print some objects. The models are classified into various categories and can be freely downloaded and printed.

Tinkercad: While Tinkercad is primarily a browser-based 3D design and modeling tool, it also has a community that shares and prints their designs.

Yeggi: Yeggi is a search engine for 3D printable models. It aggregates data from many 3D printing sites and allows users to quickly search for the best models.

3Dfindit: 3Dfindit is a visual search engine that crawls billions of 3D CAD & BIM models from thousands of manufacturer catalogs for mechanical and electrical engineering. The platform allows students and teachers to search and download free digital engineering data provided by manufacturers worldwide.

TurboSquid
CGTrader
Free3D
Sketchfab
3D Warehouse
Shapeways