Unless I want whatever I am cooking them for to be white, I use the whole leek. I cut off the really tough green bit though. I often make a side vegetable by slicing in about ½ inch pieces, saute gently in butter (or a mix of butter and oil) until nearly cooked but still al dente, add some flour to make a roux, when this has cooked out add some milk to the required consistency and add a little cream if desired. S&P to season and sometimes a little thyme. As Raymond Blanc would say "et voila".
I sometimes do this with just the green part if I have used the white for something else.