I don't think of it as memorizing a tune. I think of it as knowing a tune. Once i listen to a tune many times, and then play it many times, either alone or with others...that's when I know the tune. I might still make an occasional mistake or lapse, but I'll know it's a wrong note immediately and I'll hear in my head what it was supposed to be.
I learn tunes through several methods- sometimes sheet music, sometimes TAB, sometimes a recording, sometimes from other people playing it live with me so I can learn it. But no matter what method i use to 'catch' the tune, once I know it well I won't need to look at paper anymore.
That said, if time passes I might need a memory jog as Robin said, but usually I can pick the tune back up pretty quickly at that point, because I once knew it under my fingers.
I'm all for really knowing a smaller number of tunes, rather than half-knowing a whole bunch. I usually work on a current repertoire of about 75 tunes, putting other stuff on the back burner for a while. I don't try to 'keep knowing' everything I've ever known how to play well, and when i go back to stuff i knew in the past I often need to refresh it for a while. I've read that the great fiddler Tommy Jarrell only had a repertoire of less than 50 fiddle tunes that he played wonderfully over the years.
Those irritated by grain of sand best avoid beach.
-Strumelia proverb c.1990