Modern websites rely on data. In fact, it is difficult to find a website that does not pull data from some database or send data to some data store.
Let's look at some examples...
The Obvious Ones
Google has buildings full of data used to service your search requests, store your GMail, record your activity.
Amazon is the world's largest retail store and stores over 42 terabytes of data.
Your financial institution relies on databases to trach your money.
The Less Obvious Ones
Like all news sites, ESPN stores its stories in a database allowing them customize the way they display, group, feature, push each.
All of the top blogging platforms (e.g. WordPress, Blogger, LiveJournal, Typepad) use databases to store articles, metadata, and comments.
Dropbox, like all cloud file services, stores information about your files in a database.
What About These
What about sites like SnapChat? Even though your photos, video, and messages disappear, they are stored in databases.
SquareSpace, among others, allow you to create websites that do not appear to be data-driven, but all of the content and styling is stored in a database.
What about your school's website? Yep, powered by a database!