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1.
An informal version of "you're welcome".
Jane: Thanks for inviting me to your party, John.

John: "Hey, anytime!"
by NestlePureLife001 December 17, 2011
 
2.
The word that dumb people say to people they just met after they ask: "When can I ring you?" not even thinking that these guys could be dangerous and you're just opening yourself up to them like the giblees.
"Hey soft-breasted tender little maiden of demon worship, when may I next contact you using my telephone device?"
"Oh, anytime."
by Dylan Hewson May 30, 2005