I am looking for a list of 3D modeling programs(preferably open source) that supports exports of animations in the 3DS file format.
I have tried Blender, but it does not seem to support this feature(correct me if I'm mistaken).
Try Google Sketchup: http://sketchup.google.com/
Link to help page describing the output to 3DS: http://sketchup.google.com/support/bin/answer.py?hl=en&answer=43686
In case you don't want to pay for the Pro version: http://forums.devshed.com/game-development-141/converting-sketchup-models-to-3dst-519710.html
You will find a tutorial for Blender under the last link as well.
Unless Autodesk has rewritten the .3ds format in recent months, the format does not carry very useful animation data. Clunky support even in it's native 3DStudio. People have written workarounds in some programs that write a .3ds file for each frame of animation, but that's not a very practical or efficient means.
Why does it have to be a .3ds file?