How to write on FAT32 and NTFS from Mountain Lion? What is the best free software for OS X Mountain Lion for enabling write support for FAT32 and NTFS?
At the moment, the only free way for NTFS write access without using abandoned software is using NTFS-3G along with FUSE for OS X. There's a guide for that in the FUSE for OS X wiki.

If you need NTFS writing a lot you might be better off using Tuxera or Paragon, both commercial but more faster and more bulletproof solutions.

As pointed out in the comments, there's no write restriction for FAT32 volumes in OS X.