Morgan McGuire makes available a collection of Meshes that are common in recent papers. Most meshes are available in OBJ format.
The Brown Mesh Set, also by McGuire, provides a huge collection (1139) of older models. These models are in IFS format. Sample source code to read them is provided in the G3D engine.
The Large Geometric Models Archive provides the iconic Stanford Bunny, a large (+4 million vertices) skeleton model, and terrain data for the Grand Canyon and Puget Sound areas.