Use a single formatted text column[1] for storing the tags and use a capable full text search engine to index this. Else you will run into scaling problems when trying to implement boolean queries.
If you need details about the tags you have, you can either keep track of it in a incrementally maintained table or run a batch job to extract the information.
[1] Some RDBMS even provide a native array type which might be even better suited for storage by not needing a parsing step, but might cause problems with the full text search.
