Gaffe, with an e, means (1) a clumsy social error, (2) a faux pas, or (3) a blatant mistake or misjudgment. The far less common gaff, without the e, means a large iron hook attached to a pole or handle and used to catch large fish. In British English, gaff also means a disreputable music hall or theater.
Examples
These writers use gaffe well:
Older people have more trouble detecting social gaffes committed by others, the result of a decline in how they perceive emotions … [Reuters]
Nicolas Sarkozy, the French president, was jeered after an embarrassing gaffe in which he suggested the historically disputed Alsace region was still in Germany. [Telegraph]
And these are rare examples of gaff found in the wild:
The Tribal Warrior is a 15.4-metre gaff-rigged ketch. [Sydney Morning Herald]
The stepson said he remembered the fishing gaff hook hanging from his backside after his stepfather threw it at him … [The Sudbury Star]

