Completed and available to build, with link to CAD files and build instructions:
OSVehicle Tabby: Tabby is the first OSVehicle: an industrializable, production ready, versatile, universal chassis.
LifeTrac tractor from Open Source Ecology has build instructions for most revisions
Concept stage:
Rally Fighter, an all-terrain vehicle by Local Motors uses a design released under a CC BY-NC-SA license. The design was made piece by piece by an open community in a forum. Several units have been manufactured and sold.
Luka EV, an electric car production platform which first car is the Luka EV. Only Mrk I & II are open source, the source was closed in July 2016 to allow commercial production of Mrk III
Google Community Vehicle, a multi-purpose mode of transport. It can be used as a farm vehicle that attaches to farming equipment or as a means to transport the produce. This car was created by an Indian team for the 2016 Michelin Challenge Design, "Mobility for All International Design Competition"
Self-driving car prototypes have collected petabytes of data. Some companies, including Daimler, Baidu, Aptiv, Lyft, Waymo, Argo AI, Ford and Audi have publicly released datasets under more-or-less open licenses.
Other open-source vehicles
Many open-source vehicles come in the form of velomobiles, like the PUUNK, the Hypertrike, the evovelo mö or the Atomic Duck velomobile.