A new site in the “Haven” family of sites, 3D Model Haven is a collection of CC0 3D models in FBX and Blend formats. It’s brand new and rather limited in selection right now but is bound to grow with the support of an Epic MegaGrant.
The Unreal Engine asset store is a fraction of the size of the Unity store. The majority of free content is directly from Epic, but is of exceedingly high quality. The above link searches for just free content. Products are freely usable in personal and commercial projects as long as you use Unreal Engine.
TurboSquid is one of the oldest model resources on the internet and has a huge collection of free assets. The link above links directly to the free models, you can then filter down by addition requirements (rigged, poly count, etc)
OpenGameArt is a repository for free assets aimed at game developers. The above link is direct to the 3D objects section. This is a non-curated collection, so the quality varies massively.
This site is dedicated to Blender and contains tons of Creative Commons licensed resources. You are given a daily download limit if not a member, although a free login option exists.
Sketchfab is quickly becoming the place to demonstrate your artistic abilities, with full WebGL previews available. The above link is for resources tagged as free and downloadable. Unfortunately, their search interface makes searching for free assets needlessly complicated.
CGTrader is another online game marketplace with a large number of free downloads available. The above link is for free assets only. Be careful of licenses, royalty-free licensed assets can be used in commercial projects, while editorial licenses cannot be used in commercial products.
This is the Microsoft alternative to Google’s Poly. It’s aimed at Paint3D usage, so you have to open first in Paint 3D (a free Windows 10 only application), then export to a format such as FBX.
Yeah, that NASA. They have a large collection of space-related models and textures available. Granted a very niche collection, but invaluable if you are making a space-related game.
Another site with a huge archive of free 3D models for download. Currently over 130K models on the site.
Yobi3D (No longer available as of Jan 2019)
Yobi isn’t a model site, it’s a search engine that searches free sites. It searches several different free sites. Be aware the license varies from site to site, so be careful before using results in a commercial project.