For a web application, when creating the user which will connect to the MySQL database, you have the choice of privileges. Assuming that the only actions intended to be done by that user are SELECT/INSERT/UPDATE/DELETE, it seems to make sense to only provide those privileges, however I've never seen that recommended anywhere - what are the reasons for and against this method?
I disagree with Bill here and Atomix's line of thinking is more suitable. Unless it can be demonstrated otherwise, Bill's answer highly increases the risk of the database being compromised.
Perhaps for very experienced developers there is other security in place, but for other developers giving a script full, unfettered access to do ~anything~ to a database is asking for trouble, when there is no need to.
The principle of least privilege should be in use here. For MySQL, have a super user with all privileges which is used for creating tables, drop database, and so on. Ideally this username and password is never seen in any PHP file or any file on the web server. (I'm using PHP as an example but it applies to other web applications). You would only use this username and password with something like PHPMyAdmin or MySQL Workbench.
Then, for PHP scripts, have one with the minimum required, such as just INSERT, SELECT, UPDATE, maybe not even DELETE, depending on your PHP script. This would be in the PHP files, that is, actually only ONE file OUTSIDE of the document root, as is recommended by most.
The reason is thus: yes, you do not need a MySQL user for every web application user. But principle of least privilege ( http://en.wikipedia.org/wiki/Principle_of_least_privilege ) should apply. If somehow your MySQL super user is compromised because you accidentally named your MySQL connect script as .txt instead of .php, or someone gained access to the web server files, at least the "worst" they can do is SELECT, UPDATE and INSERT... Which while can cause big problems anyway, is not as bad as giving them DROP DATABASE, DROP TABLES and much worse things.
Additionally, in my current project due to agile development practices (I do not work for but recommend http://www.agilealliance.org/)