You like the default front page view, but you find you want to sort it differently.
You like the default taxonomy/term view, but you find you want to sort it differently; for example, alphabetically.
You use /tracker, but you want to restrict it to posts of a certain type.
You like the idea of the 'article' module, but it doesn't display articles the way you like.
You want a way to display a block with the 5 most recent posts of some particular type.
You want to provide 'unread forum posts'.
You want a monthly archive similar to the typical Movable Type/Wordpress archives that displays a link to the in the form of "Month, YYYY (X)" where X is the number of posts that month, and displays them in a block. The links lead to a simple list of posts for that month.
Views can do a lot more than that, but those are some of the obvious uses of Views.