When should I build the Crane card?
The crane can be very useful when you don't want to finish the game.

Remember: the one who builds his/her 12th building isn't the winner. This action only ends the game. If you have 11 houses and are not in a position of wining, it could be useful to build one more without finishing the game.



EDIT

Also, using a crane can help you building a big house in two steps, no need to have seven cards in the hand at one time.

An interresting effect linked to the use of the crane is that you can use the builder's privilege twice on the same card. Let's say you want to build something that is worth 6. You are the builder. Build some building that's worth 3, pay it 2. Next turn, choose the builder, expand your 3-building to your 6-building, pay 2 instead of 3. The total cost of the building was 4 instead of 6. Add to that some additionnal cards that reduce the price, you can even have a free 6-cards!!!