Mongodb dynamic like operator

One way to do it, according to the documentation page:

db.users.find( { shows : { $regex : letter } } );

+1 for mindandmedia on the syntax. However, please remember, that if you want the query to use an index efficiently, you have to use prefix queries (also called rooted regexps) like /^prefix/

Your query is likely to be horribly slow otherwise - see the note in the docs here:

http://www.mongodb.org/display/DOCS/Advanced+Queries#AdvancedQueries-RegularExpressions