I wouldn't choose whether to use an SQL database based on how much data I wanted to store - I would choose based on what kind of data I wanted to store and how it is to be used.
Wikipeadia defines a database as: A database is a structured collection of records or data that is stored in a computer system. And I think your answer lies there: If you want to store records such as customer accounts, access rights and so on then a DB such as mySQL or SQLite or whatever is not overkill. They give you a tried and trusted mechanism for managing those records.
If, on the other hand, your website stores and delivers unchanging file-based content such as PDFs, reports, mp3s and so on then simply storing them in a well-defined directory layout on a disk is more than enough. I would also include XML documents here: if you had for example a production department that created articles for a website in XML format there is no need to put them in a DB - store them on disk and use XSLT to deliver them.
Your choice of SQL or not will also depend on how the content you wish to store is to be retrieved. SQL is obviously good for retrieving many records based on search criteria whereas a directory tree, XML database, RDF database, etc are more likely to be used to retrieve single records.
Choice of storage mechanism is very important when trying to scale high-traffic site and stuffing everything into a SQL DB will quickly become a bottleneck.