An example of modifying a MySQL table to increase a VARCHAR column size:

alter table TABLE_NAME modify COLUMN_NAME VARCHAR(1024) NOT NULL;

This increases COLUMN_NAME to 1024 characters.

In MySQL 5.0 it is possible to drop unqiue constraints but, the syntax is not incredibly intuitive.

alter table TABLE_NAME drop index UNIQUE_CONSTRAINT_NAME;

Code Ghar provides a more thorough description.