What is the replacement for uniqueidentifier in Mysql

According the MySQL website you should match it to VARCHAR(64)

UNIQUEIDENTIFIER,   VARCHAR(64)

http://dev.mysql.com/doc/workbench/en/wb-migration-database-mssql-typemapping.html

CREATE TABLE FOO (
myid CHAR(38) NOT NULL,
barid CHAR(38) NOT NULL
);

According to MS website, GUID's are 38 chars in length.

The accepted answer, although not exactly wrong, is somewhat incomplete. There certainly are more space efficient ways to store GUID/UUIDs. Please have a look at this question: "Storing MySQL GUID/UUIDs"

This is the best way I could come up with to convert a MySQL GUID/UUID generated by UUID() to a binary(16):

UNHEX(REPLACE(UUID(),'-',''))

And then storing it in a BINARY(16)

If storage space of the GUID/UUID is a primary concern this method will deliver significant savings.