You'd think that importing .3ds files into Xna would be a common enough operation that a quick search would come up with a solution. Think again. I wasted a whole morning trying to find a working method. After a bunch of dead-ends, I finally found the Autodesk FBX Converter.
You can download it here.
It purports to convert .3ds, .obj, .dae, and .dxf files to .fbx, but so far I've only tried .3ds.
Note that I had to select FBX 2010 as the destination format, as the default of FBX 2011 didn't work for me.