If it's a digital download you might be able to go into your purchase history and get the key otherwise you need the box or manual with it on. No other way as I know.
It's amazing how many people "lose" their serial #'s!
How does that happen, exactly?
"My mortal enemy, Lord Battenbottom, sent his trusty falcon through my window at the exact time the window screen cleaning service had just removed all the window screens! I lunged at the raptor, but, alas...to no avail as the feathered demon separated my Trainz disc from it's packaging and then made off with the documentation! Off in the distance I could hear Lord Battenbottom snickering with great abandon..."