Gimmie is an agreement made between players during Match Play when a putt that has one side has conceded to an opponent side. Usually very short putts are conceded as a sporting gesture and as recognition that the side would have holed the putt.
Not allowed in Stroke Play.
There are no rules about gimmies as to what is an acceptable length. It is considered rude to request a gimme. It is completely up to the discretion of the opponent however, and he is perfectly entitled to never give a gimme.