A controlling interest is an ownership interest in a corporation with enough voting stock shares to prevail in any stockholders' motion. A majority of voting shares (over 50%) is always a controlling interest. When a party holds less than the majority of the voting shares, other present circumstances can be looked to determine whether that party is still considered to hold a controlling ownership interest.
In the United States, Delaware corporations have a 2/3 vote requirement for a motion to pass. In theory, this could mean that a controlling interest would have to be over one third of the voting shares.