I found the Autodesk FBX Converter 2013, it's only 100MB, but it allows you to convert FBX files exported from Blender to FBX 2009 format without installing 3ds Max. Of course, there's also FBX 2006, but the import plugin in Maya 6.0 is bad; it breaks the bone bindings, so you need to use the 2009 version... I think someone already mentioned this, but I don't remember who.
Wow, does this mean we can ignore 3ds Max?