This has been a long standing issue with trying to get rigged and animated models from Maya into the game engine.
The only advice I could give you is keep the rig simple and use rotational keying only. Out of the 25 or so models that I have tried to convert from Maya only one was succesful. I dont use Maya, I only use 3dmax to animate the models from artist that we get characters from Maya. I have been trying for a year or better to get the direct animation from maya into max and then into xfile format.
There is no animated xfile format export for Maya as of yet.
Must export to FBX format and bring it into 3dmax, Strip out the extra Maya stuff, and then export to xfile format using Pandasoft exporter. Most of the time there are scaling issue that have to be dealt with and when I try to rescale it in Max, it does with great pain and time, then it seems like any props or weapons dont follow the model once it is in 3dmax.
.obj format unfortunatly does not transfer the bones or animations either.
As far as static object from Maya, export to fbx or obj file and use one of the methods listed from mickyb.
This method was discovered from one of our animator using Maya, But I dont know enough about Maya to make it work. Maybe you will have better luck then I did.
I probably found a way how to convert models (with animations) from Maya to FPSC (perhaps I was late and you have found your own way already). Ok, I'll try to describe my way. I have not tested it personally, but I think it should work, but apart from Maya, you will need the 3DS Max too (I suppose the 3ds Max is your main tool, therefore you have it). Now, only what you will need is so-called "ActorX Importer" or UDK importer-exporter both for Maya and 3DS Max.
Check the following links: http://www.gildor.org/downloads <---There you'll find ActorX Importer for 3ds Max
http://udn.epicgames.com/Two/ActorXMayaTutorial.html
http://udn.epicgames.com/Two/ActorX.html#Maya%20Exporter%20Plugins
There you should find some working exporter for Maya
I was testing ActorX Importer for 3ds Max and worked great, therefore Maya version should work fine too.
My plan is easy. You are opening your Maya model in Maya, and then converting to UDK file format. UDK supports a two file formats, namely PSK for meshes and PSA for bones with animations. Now, this converted model you have to import into 3ds Max by using ActorX Importer. When you'll do this, you'll need only export your model (which was imported before the moment) to .X format by using Pandasoft exporter.
I only tested ActorX Importer for 3ds Max as I wrote before, because I don't have Maya. However if this plugin works very well in 3DS Max, should works well in Maya too. My main program for animating and then for exporting is Fragmotion but I use 3DS Max from time to time.
