Which is correct, "He dove into the water" or "He dived into the water"?

Dive, which was originally a weak verb, developed a past tense dove, probably by analogy with verbs like drive, drove. Dove exists in some British dialects and has become the standard past tense especially in speech in some parts of Canada. In the United States dived and dove are both widespread in speech as past tense and past participle, with dove less common than dived in the south Midland area, and dived less common than dove in the Northern and north Midland areas. In writing, the past tense dived is usual in British English and somewhat more common in American English. Dove seems relatively rare as a past participle in writing.

http://www.merriam-webster.com/dictionary/dive

This is a matter of local usage. In England or elsewhere in the UK "dove" would sound distinctly odd, although as we are used to American forms of English it would be understood. "Dived" would be the normal usage.