Use mysqldump to dump the database into a text file, like this:
mysqldump.exe databasename -u username -p > "c:\\databasedump.sql"
Then search using a good text editor.
If you're on linux, you can pipe the output to grep and/or awk and all that stuff too.
PS: this will only work if the string is cleartext. (not encrypted or encoded in a strange way)