Yep. The st and ct ligatures aren't much used in modern typography (I've got a newspaper that does it in its weekend extras), but fi, ffi, fl are pretty common, and fj and ij in certain languages or fonts. If you take a look at this article promoting LaTeΧ, you'll see it compares MS Word's inadequate handling of ligatures:
to how Latex does it:
and it includes images of other, optional ligatures, like ct and st:
The thing with ligatures is in the way printing used to be done, with metal blocks, a ligature would be a single block rather than two separate character blocks:
So it both looks good, and lets you use fewer metal blocks when printing common character combinations, i.e. if you didn't have any fi ligatures you'd have to have more f and i blocks to compensate, or possibly do something else, more complicated, to get all the letters onto the page.
Next up in the history of printing: Why do we use the terms "lower case" and "UPPER CASE"? Were the upper-case letters stored in a case above the lower case ones?