I believe Facebook restricts
membership to 13+. Should I have this
restriction too?
Most likely, yes - particularly so if your target audience includes minors in the United States or Australia. (and, really, anything that 14 year olds like will probably be popular with some 13 year olds, too)
I'd highly recommend a review of COPPA.org and a cautionary note from the Wikipedia entry for COPPA:
This is an American law, however, the
Federal Trade Commission has made it
clear that the requirements of COPPA
will apply to foreign-operated web
sites if such sites "are directed to
children in the U.S. or knowingly
collect information from children in
the U.S."
. . .
The website Xanga was fined USD $1
million for COPPA violations, for
repeatedly allowing children under 13
to sign up for the service without
getting their parent's consent.
Similarly, UMG Recordings, Inc. was
fined USD $400,000 for COPPA
violations...
To avoid any potential liability, it would be best to talk with a lawyer if you plan to collect and store minors' personal information and particularly if you plan to market to minors.