As a buyer of website design services for corporate clients, I would reject
out of hand a designer who did NOT use a contract -- either his/hers or
mine.
In the United States, a visual design belongs to the designer unless it is
done as a "work for hire" or ownership is formally transferred to the
client, normally through a written agreement (a contract.) If I neglected to
obtain the intellectual property rights for my client I would be guilty of
malfeasance.
Similarly, the designer and the client both need to know the scope of
work -- will the designer create a template, several templates (home and
interior pages), place the content on the pages, provide admin or CGI
software, arrange for hosting, set up e-mail accounts, manage content
updates...
What is the schedule? When is the first concept due? When is the final
design due? When is the completed site expected to go online? Is there a
penalty for a delay? Is there a bonus to the designer if the client requires
more design iterations, or is slow to respond to the designer?
What happens if the client doesn't pay, or doesn't like the work? A right to
sue means the designer has the "right" to wait months or years for a court
date, and the "right" to pay an attorney. A contract with a mandatory
arbitration clause short-circuits that kind of delay and expense.
In short, use a contract!
Alex