What is the fastest refresh rate of an Arduino?

I think I'm looking for the fastest sample rate when using just one pin of the analogue in pins? :~
Basically I need the quickest possible way to receive real world analogue information process it and then send it digitally onto another application within my computer?
I'm wondering if this is indeed possible with the Arduino without any noticeable latency what so ever?
Hope this is possible?

Thanks for the quick reply

izzi