Model
Start with obj and then add things
3D formats based around surfaces such as triangles and other polygons. The format categories are listed on the software formats page.
Tools
Exchange
DAE (COLLADA) - http://collada.org
Interchange format for 3D applications managed by the Khronos Group.
glTF
Why we should all support glTF 2.0 - 2017
Comparison of OpenGEX, Collada, and glTF
FBX2glTF
https://github.com/facebookincubator/FBX2glTF
Format owned by Autodesk that is used for interoperability between digital content creation applications.
Immediate
Game
nif - http://niftools.sourceforge.net/wiki/NifTools
mdl (quake) - http://tfc.duke.free.fr/coding/mdl-specs-en.html
MD2 (quake2) - http://tfc.duke.free.fr/coding/md2-specs-en.html
MD3 (quake3) - http://www.icculus.org/~phaethon/q3a/formats/md3format.html
MD4 (quake3) - http://www.icculus.org/~phaethon/q3a/formats/md4format.html
MD5 (doom3) - http://tfc.duke.free.fr/coding/md5-specs-en.html
Obsolete
3DS - 3D-Studio File Format
https://code.google.com/p/lib3ds
http://www.fileformat.info/format/3ds/egff.htm
http://paulbourke.net/dataformats/3ds
ASE - 3D Studio Max Ascii Export Format
http://paulbourke.net/dataformats/ase/
Lightwave 3D Object File Format
http://paulbourke.net/dataformats/lightwave/
OBJ
Wavefront .obj is text format for simple 3D geometry. It can contain vertex, UV position, vertex normals and faces made from these. Faces can be assigned to named objects and groups. As most OBJ writers/readers only support absolute indices it is not possible to merge two OBJ files by copying one into another. For that tools need to be used that rewrite the absolute indices.
Native
Reference