Most people tend to not see an epic item until they hit 60 and start hitting raid content, although there are a few low level epics to be found in the world.
Personally, I was lucky, I got my first epic at level 55, I remember the day well. I was questing in Burning Steppes, looking for Blackrock Medallions I recall, and I killed a Blackrock Worg that dropped a Hurricane bow. Needless to say everyone in guild chat heard about it instantly and the item got linked to all who were not there for the momentous occasion as soon as I saw them online.
Unfortunately, the Hurricane is a pretty weak epic by most standards, but at the time it was quite thrilling, not only to get an epic but one I could actually use.
The thing goes through arrows like crazy but I still have it, though I don't really use it anymore. Of course I have many more epics now but that one still stands out in my mind.
Anyone else have a fond tale of their first epic moment?