There is no need for a (written) contract, where both parties are honorable and everything is patently obvious. Indeed, I'm able to do a lot of my work on even less than a handshake.
Verbal discussions can be considered as a contract, but it gets a lot trickier determining who meant what.
The best written contract isn't worth the paper it's written on, if one of the parties is a scoundrel.
It's for that middle ground that we need pieces of paper. They help define the scope of the job, the amount to be paid, and all the other niggling details that come along. This is especially important where there are multiple parties involved, or there is a change in personnel.