Solution 1:

The British National Corpus has 5445 cites for grey and 1092 cites for gray. The Corpus of Historical American English, on the other hand, paints the following picture:

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(X axis: year, Y axis: incidences per million words.)

After seeing these stats, it should come as no surprise that Wiktionary marks grey as British, Canadian, and gray as US.

Solution 2:

I grew up in England for chunks of my childhood and early adulthood and am still around people who originated from the UK, so I still encounter both spellings all the time. The easiest way to remember it is that the 'a' in gray stands for 'America' and the 'e' in grey 'England'.

Solution 3:

I have found out about Google NGrams. It is really useful for such questions. The gap between the two spellings was important during WWII, then was really narrow, and finally it has been widening since the 1980s.

American English: "grey" vs. "gray" ngram graphBritish English: "grey" vs. "gray" ngram graphEnglish (cumulative): "grey" vs. "gray" ngram graph

Solution 4:

According to the Associated Press (AP) Styleguide, 'grey' is only used in the word 'greyhound' -- otherwise the appropriate use is always 'gray'. In America, anyway.

Solution 5:

In addition to the other answers correctly stating that grEy is British English and grAy is American English...

Proper names (capitalized Gray) in British English (red line) account for more than 50% of the instances of the American spelling, Gray.

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N-grams link