This page was last updated February 2017. If you know of any sites with free models, please drop a link in the comments!
123D - This site is Autodesk's online suite of tools for modelling and 3D printing, but the site also hosts a modest but rapidly growing gallery of designs uploaded by users that can be downloaded by other site members.
3D Burrito - a 3D designs marketplace focused on hobbyists and amateur designers. This is among the least reliable markets out there, as file entries frequently include little to no information about the design specifications.
3D Content Central - 3D ContentCentral hosts free 2D and 3D CAD files from engineers and firms. You can also request models.
3D Parts Database - The Shapeways 3D parts database is a place where you can download free 3D models free for 3D printing. The files currently in the database have all been tested and printed by Shapeways and all “print for sure.”
Archive 3D - an extensive collection of furniture models and the only 3D printable Lute I've ever found.
Artist-3D - I have found a perfect modelling site it does textures models everything you will need, and of course, its free.
CG Trader - a 3D model marketplace for computer graphics and 3D printing founded in 2011 and backed by a strong designer community. CG Trader offers both free and paid models, printer ready and incomplete designs.
CubeHero - this is my favorite 3D designs repository, at the moment. It offers an integrated versioning system that allows users are able to see changes that have been made to a 3D file, which makes collaborating as a community much, much simpler. There are still only about a hundred models on offer, but by offering their services and files for free, they're guaranteed to grow.
DEFCAD - Operated by Defense Distributed, this site is a makeshift response to Makerbot Industries’ decision to censor firearm-related files on Thingiverse. They are hosting as many of the files pulled from Thingiverse, occasionally adding more.
GitHub - Yes, that GitHub. Everyone's favorite code repository is also an excellent place to browse 3D printer designs. GitHub integrated a 3D viewer for .stl files a few months back, and the response was overwhelming. There are now over twenty thousand files ready to download.
GrabCAD - GrabCad is a site for engineers to show off and share their CAD works, with over 75,000 free models available. There is an .stl filter available.
Instructables - this DIY project community offers quite a selection of 3D printing projects. The site's instructions often come with .stl files. User the “3D printing” tag to find projects for your printer.
My Mini Factory - A site from iMakr offering a nice selection of free 3D Printable objects. What sets this site apart from the rest is that it claims that all of its designs have been test printed by their team, which means you're not going to waste time printing out someone else's mistake.
The Pirate Bay - Since the creation of its “physibles” category, many new 3D designs have been uploaded to the Pirate Bay.
ShareCG - ShareCG.com hosts the web's largest collection of free Computer Graphics resources including thousands of free 3D CG Models
Sketchfab - a library of downloadable 3d model from dinosaurs to Minecraft cathedrals. All of them are downloadable under Creative Commons licenses, most of them are printable.
TF3DM - Tf3dm.com or "the free 3D models" boasts almost five thousands models.
Thingiverse - Thingiverse is a huge community of people who create and share 3D designs freely, so that all can benefit from them. Widely used by the RepRap Project, and by 3D Printer and MakerBot operators.
Trace Parts Online - TracePartsOnline.net is one of the biggest parts libraries in the world, offering 100+ million free 2D drawings & 3D CAD files.
Trimble 3D Warehouse - The Trimble 3D Warehouse (formerly Google 3D Warehouse until purchased by Trimble) is an accompanying website for SketchUp where modelers can upload, download and share three dimensional models. This is an especially good place to look for models of famous buildings, as SketchUp interacts with Google Earth.
TurboSquid - TurboSquid is a large repository of both pay-for and free 3D models. There’s no area dedicated specifically to 3D printing, but users can search the site by file type, such as .stl and .sldprt (Solidworks part).
Yeggi - a meta search engine for 3D printable files. It aggregates content coming from 3D printing repositories such as Thingiverse. It's not the first such search engine, but at the moment, it's clearly the best. I suspect that, as 3D print grows in popularity, the competition is going to be fierce.
Yobi3D - finding the 3D model you're looking for can be a time-intensive undertaking. That's one of the reasons I assembled this directory, in fact. Yobi3D looks to simplify matters by serving as the Google of the 3D printable world. It has a keyword search interface, but after entering a search term, an infinite scrolling grid of thumbnails representing 3D models found on a diverse collection of websites is shown. By clicking on one of the thumbnails, users can see a 3D rendering of the model right away. They can use the mouse to rotate and move the 3D model around to see from different angles and zoom distances.