I've been on different mission trips, but have never dreamed about asking people to help finance them. However, I have donated to others going. I think it's great for teens to go whether it's helping with building projects, orphanages or otherwise. It really gives them appreciation for the things they have. Years ago our 12 year old son commented how appreciative the children were and that, unlike Americans, there's no sense of entitlement.
Nowadays if I was going to donate it would be for services rendered--cleaning, yard work, etc so that also becomes a learning experience.