I can’t raise them on this computer, but we all know them: the single-character ligatures for fi, fl, ff, ffi, andffl. We never see them in print anymore. Why? Are the computer-using typesetters too lazy to retrieve the ligatures? Or do all such computers lack the character map like the one I’m using does?
And in all of Cecil’s Straight Dope books in the 90s, the lower-case italic j (Caledonia font) has a downstroke with a “ball” at the end; in Return of the Straight Dope, as in most usages before 1988, the letter’s downstroke looked like a slightly curved dagger blade. Is this a function of political correctness? 
I see ligatures all the time in formal ads. Not text, granted.
Most of the “serious” font systems and art packages allow for them, at least if you look at the boxes. I’ve never been able to justify paying for something fancy myself, but as a student of calligraphy I love to dream.
You know, part of the problem may be the keyboard. Europeans are used to having to deal with multiple keystrokes to get all their accents, but in English, we don’t have to.
If you’ve seen a Linotype machine, they have the ligatures as separate keys, so any fontmaker had to produce something that printed when those keys were pressed.
MS Word (97 and later) is supposed to automatically substitute the ligature when the appropriate combination is typed.
A few years ago when I used Quark Xpress regularly, (IIRC), it automatically substituted ligatures for the appropriate combinations of letters. Nowadays, writing and typesetting aren’t as separated as they were for the previous 550 years, people are using their word-processing programs as their publishing programs, and Word just doesn’t do this. (Also, the expert typesetter of old who used to pick up the ligature block as a matter of course just isn’t around anymore.)
–Cliffy
Some fonts simply don’t have the ligatures in their character sets. If the font designer didn’t create ligature characters, then there’s no ligature character to insert or replace the nonligatured characters.
I have many fonts that contain only the standard lowercase and uppercase letters, punctuation and numbers. If you try to type anything else, an open square character appears in its place. When this is the case with the font you’re using, all you can do is 1) hope you can find a clone that does have the character you need, 2) substitute another font’s character in its place and hope no one notices or cares about the difference, or 3) pray you never need those special characters, ever. 
Fonts designed by reputable foundries are likely to have full character sets, which can contain more than 200 letter, symbol, and punctuation characters. Inexpensive fonts, novelty fonts, and decorative fonts are less likely to have full character sets. I think this can be attributed to both font designers too lazy to design full character sets, and some font designs not lending themselves well to the design of special characters.
Still, I think the main reason you seldom see ligatures used is because publishers don’t know about them or care if they’re used. They are more for aesthetics (I wish I could type the ae ligature!) than basic readability, and I think that gives them a lower priority. Rightfully so, but it still would be nice to see them used more often.