Database structure for tags?
It makes sense to store tags themselves in a separate table, and add a link table to implement many-to-many relationship between users and tags, for example

users (user_id (PK), name, [other user attributes]);
tags(tag_id(PK), tag_name, [other tag attributes]);
users_tags(user_id (FK to users) ,tag_id (FK to tags), PK(user_id,tag_id));


Depends on your needs, users_tags may have other attributes as well, for instance you might want to add datetime column to store when user added tag (surely, if it has any value to your application)