The answer to this is two-fold.
Yes. MySQL _DOES_ allow the creation of foreign key constraints
(see http://www.mysql.com and search documentation for the syntax and other information).
However, FKs are only ENFORCED with InnoDB (the default table-type is MyISAM) tables at present. There is a task added to the TODO list for a future version (5.0 or 5.1, I believe) to add full integrity checking on FKs to all table types.
If you require integrity checking via FKs you MUST use InnoDB format tables. MySQL also requires that you manually create an index on columns which are to be referenced in FKs (both the reference column and the referring column) for speed of queries/joins.