Reading your comment,Malvin, was better to post this as a new answer:
Malvin, OBJ is quite used for static models. But for character animations, you need to be able to transport bones information, and vertex weights (the value with which each vertex is influenced by several bones, or only one, or none). Also constraints info, in some cases. That all would be the "rigging" info, basically. Then there's animation info needed, like keyframes (frames where some change happens), interpolation type between them, etc, etc. All these is not supported by OBJ. A good, lightweight and practical format for this is *.md5 , but is probably more recommended Collada, which is becoming a very adopted standard and that can port everything, from statics, scenery, to character animation. It is supported by the big ones: Maya, Max, XSI. Blender is supporting it but not yet fully. The collada issue is that is complex to make yourself a loader, as is a very complete format, and for this reason, several packages don't have a fully functional exporter for this. Still, might be the way to go.
You can of course dump OBJ frames from an animation package, and then interpolate in the engine, as exporting one obj per frame would be too much heavy and costs memory. Maybe one every 2 or 4 frames...
You can also use FBX for character animations, but my advice would be using collada instead of it.
First of all, check if your artists are going to be able to export in whatever the format, from their package. Otherwise is a hard to solve problem. Indeed, make complete tests of features ported and and confirm is working in your engine.
About what people is doing, in my experience, all of this... But in game companies, often just they do a converter from whatever format to a custom, native, binary format for their engine. Optimized and faster to load, etc.
I have done prototypes or even games just using OBJ or ASE and md5 for animations..Depends on artists workflows, toolset, etc.
Edit: Sorry, seems Fuzzy had already answered several matters. Agreeing there.