When vehemently agreeing with something someone said, is it correctly "HERE HERE!" or "HEAR, HEAR!" or what?

hear, hear:

(idiomatic) Expression of support, agreement, or enthusiasm for what has just been said, as after a toast.

http://en.wiktionary.org/wiki/hear_hear

Meaning: A shout of acclamation or agreement.

Origin:

Originated in the British parliament in the 18th century as a contraction of 'hear him, hear him'. It is still often heard there although it is often used ironically these days.

http://www.phrases.org.uk/meanings/178100.html

Hear hear is an expression that originated as hear ye, or hear him, usually repeated. This imperative was used to call attention to a speaker's words, and naturally developed the sense of a broad expression of favour. This is how it is still used today, although one can always vary one's tone to express different sentiments; the Oxford English Dictionary noted around the turn of the century that the phrase is now the regular form of cheering in the House of Commons, and expresses, according to intonation, admiration, acquiescence, indignation, derision, etc.

As a parliamentary cheer, hear him, hear him! is first recorded in the late 17th century and continued into the 19th; the reduction to hear! or hear, hear! occurred by the late 18th century. However, the use of the verb hear as an imperative meaning listen! is older: a notable example is the parliamentary-sounding Then cried a wise woman out of the city, Hear, hear (2 Samuel 20, verse 16) in the King James Bible, first published in 1611.

Aside from the interjection, a number of other grammatical forms are found, such as a hear, hear (originally, of course, a hear him or hear ye), meaning 'a cheer'; to hear-hear, meaning 'to shout "hear, hear!"'; and hear-hearer, meaning 'a person who shouts "hear, hear!"'.

http://en.wikipedia.org/wiki/Hear-hear

It's "Hear here!"

Like you're calling other people to listen.