Mild British expletive, thought to be a corruption of "Blind me". Sometimes seen written as "Gor blimey!", which seems to be "God blind me".

Example usage:
"Gor blimey! What time do you call this then?"

One of those words that sometimes mystifies Americans, such as git, tosser, wanker and bollocks.

In spite of what Americans may think, the image of Englishmen - and particularly Londoners perpetrated by Dick Van Dyke in Mary Poppins does not exist (especially not with that godawful accent). 'Blimey' itself is not particularly common, but it can occasionally be heard.

Confession time: I've got into the habit of using 'blimey' myself. I don't know why.