This could be...

• Proportional editing, (disable in 3d view header)
• Objects can share an action (shared animation data), (check the action space with each object selected)
• a constraint, check object constraints
• a driver (unlikely this would be setup by accident, but drivers c an do this still)

This could be...

• Proportional editing, (disable in 3d view header)
• Objects can share an action (shared animation data), (check the action space with each object selected)
• a constraint, check object constraints
• a driver (unlikely this would be setup by accident, but drivers can do this still)