Maya can export to various formats. Nowadays, mainly FBX is used because it's supported by many art packages.
If you're writing an application in c++, there's a FBX Api you can use to read fbx files:
http://usa.autodesk.com/adsk/servlet/index?siteID=123112&id=7478532
I think XNA uses this sdk in the background in it's content pipeline. (If you're familiar with xna)
There is also a Python library which can be handy to extract just the data you need from the fbx file: http://download.autodesk.com/us/fbx/20112/FBX_SDK_HELP/files/WS73099cc142f48755-751de9951262947c01c-6dc7.htm
You could also write your own export script in Maya using python, but be aware that this is not a straightforward task.
I'm sure if you google a bit, you'll find importers for other formats like .obj
which is also commonly used.