If you are already familiar with 3D printing, then Makerbot Thingiverse is probably your go-to location to find models. Thingiverse has all sorts of objects, from art to gadgets, with new submissions flowing in constantly. While Thingiverse is awesome, I'm always looking for new things to try to print. In my search to find odd/obscure objects, I have found some great 3D print exchanges hosted by museums and government organizations. Links and excerpts from each organization's mission statement are below (if you know any others, let me know!):

National Institue of Health's 3D print exchange

Few scientific 3D-printable models are available online, and the expertise required to generate and validate such models remains a barrier. The NIH 3D Print Exchange eliminates this gap with an open, comprehensive, and interactive website for searching, browsing, downloading, and sharing biomedical 3D print files, modeling tutorials, and educational material.

Examples:

3D model of a rat rat skeleton 3d model of a Raspberry Pi Scope 3d model of a Human Papilloma Virus

Smithsonian X 3D 

The Digitization Program Office is the hub for the Smithsonian’s inquiry into 3D. We support all 19 museums, 9 research centers and the National Zoo in their quest to increase the quantity and quality of Smithsonian digital assets.

Examples:

3D model of Abe Lincoln's head 3D model of a mammoth 3D model of a crab

African Fossils

African Fossils seeks to increase public knowledge about prehistory by harnessing modern technology. Through digitizing otherwise inaccessible discoveries, African Fossils is dedicated to creating a growing repository of 3D models of significant fossils and artifacts, thus making them freely accessible to all. By allowing members to share their 3D printed creations, we hope to aid teachers, students and enthusiasts to exchange ideas and to be inspired to think about our tenuous place on the planet.

Examples:

3D model of a buffalo 3D model of a mountain gorilla 3D model of harpoon head

The Virtual Hampson Museum

The Hampson Museum Collection represents one of the world's most extraordinary collections of American Indian artistic expression as well as a major source of data on the lives and history of late pre-Columbian peoples of the Mississippi River Valley. The collections at the museum are the result of extensive excavations of the Nodena Site as well as excavations at other sites in the region by Dr James K. Hampson, as well as work by others including the University of Alabama and the University of Arkansas.

Examples:

3D model of pottery 3D model of pottery 3D model of pottery

Lincoln 3D Scans

The project aims at making the collection available to an audience outside of its geographic proximity and to treat the objects as starting points for new works. All models can be downloaded and used without copyright restrictions.

Examples:

3D model of an elaborate European stone carving 3D model of Einstein's head 3D model of a man with a hunting dog

NASA 3D resources

...a growing collection of 3D models, textures, and images from inside NASA. All of these resources are free to download and use.

Examples:

3D model of new horizons space craft 3D model of Voyager satellite 3D model of block island