Are there any free/relatively cheap modular 2D sprites generators automated similarly to the likes of Fuse? Would be great if they provided the rig (or the possibility to export finished animations?) as well just as Fuse does. Does anything like that exist?

A lot of the free ones are bad however there are always new ones popping up, you should search around the web for one.

If you have some programming skill, you can make your own. It's a good practice program and doesn't take to long to make.

Cocos2d has great builtin tools for sprite animation, my own sprite generator is made from it. They also allow you to use "bones" like 3D animation.