Which one of the following sentences is correct?
- Here is the details you requested.
- Here are the details you requested.
Therefore, "Here are the details you requested" is the correct one.
As noted by Colin Fine and Kosmonaut in their comments below and by Piet Delport in his answer, "here is [plural]" is commonly used in casual English. Maybe it is more used than the grammatical form where the subject agrees with the verb (to be confirmed). Refer to Piet Deport's answer for a possible explanation.
Ralph Rickenbach is right: this question is not really about "details", but about the phrase "Here is ...".
"Details" is definitely plural: you'll say "The details are ...", never "The details is ...".
"Here is ...", on the other hand, is very closely associated with the contraction "Here's ...", and is commonly used even with normal plurals (instead of the cumbersome "Here're ..."):
Say them to yourself and see if they sound correct to you.
To me, here are the details you requested will always sound "correct". I might say here's the details you requested conversationally or in an informal setting, but I can't see Here is the details you requested ever being right.