The many ligatures used, along with innumerable abbreviations, in writing the Greek and Latin alphabets in the Middle Ages were in fact medieval innovations, and not characteristics of original writing practices in either Greek or Latin. Literacy was much less widespread in the Middle Ages than in the preceding Classical period or in the succeeding periods. The Middle Ages was a time when writing could be treated as a code, for use by a small class of people with a good deal of time on their hands, and no need for rapid and accurate reading of complex material in situations in which error had consequences.
    With the discovery of printing came the proliferation of books, readers, and demanding subjects to read about. It was at this point that tolerance for the scribal ligatures ceased: those ligatures had existed in large part for the convenience of scribes—saving them many penstrokes, saving expensive parchment, and giving them options for reducing word length to aid spacing and justification. (They had other functions as well, which are no longer needed—see below.) Some of those options were useful to printers, but they were not worth the cost of cutting punches for and fitting dozens of extra characters, and then storing them, and distributing them after each use.
    (The common f-ligatures were preserved because they have a real typographic function. The shape of ’f’ requires that the top curve be extended enough to be easily distinguishable without looking odd. Unless special forms—ligatures—are used, this causes crashes or awkward juxtapositions of shapes when ’f’ is followed by tall letters, as it frequently is.)
    Printed books aren’t as bad, since there were limits on how many ligatures could be made into type. Knowledge of a few dozen ligatures will get you through most early printed books in the Roman alphabet, though you’ll still have to exercise your knowledge of the language to figure out some of the signs. You may also occasionally have to consult Cappelli (below). Once in a while, you will still be left in doubt, because the ligatures were much less standardized than were the letters of the alphabet, so the same ligature might have multiple meanings, and multiple ligatures might have the same meaning. (This is, of course, another reason not to equate the ligatures with letters of the alphabet, as a few typographic dilettantes actually do.)

Ligatures and abbreviations also played a role in the evolution of ways to better distinguish units of meaning in text, which made it easier for the eye and the mind to recognize and process those units—which made reading easier. Ligatures and abbreviations were used only at the ends of syllables and words (later only at word-endings), and arose, along with varying amounts of spacing between syllables and words (less between syllables, more between words, later only between words). Ligatures, abbreviations, and spacing thus became means of separating syllables and words. Practice varied over time, and between regions at any given time.
    By the end of the Middle Ages or the early Renaissance, the modern practice of spacing between words became the universal standard. At this point, ligatures and abbreviations became superfluous as means of dividing text into processing units: whatever advantage they had was largely duplicated by the word spaces; any remaining advantage was outweight by their disadvantages: ambiguity resulting from the multiple meanings that many of them bore, the vast extension of the number of character forms the reader had to know and recognize, and the extra effort needed to distinguish their often complicated forms. To these disadvantages were added, with the invention of printing, the considerable expense and time of cutting punches, casting, storing, composing, and distributing all those extra characters.
    (See, in particular, Saenger, Space Between Words, pp. 40ff; the book is noted on the Reading page.)

Below, on this page, I’ve placed two tables, one of common Latin ligatures, and one of common Greek ligatures.

There’s a chapter on ligatures and abbreviations in Ullman, Ancient Writing and its Influence.

The definitive reference is:

LATIN LIGATURES USED IN MANUSCRIPTS
AND EARLY PRINTED BOOKS

Here’s a table I made for my own use. It includes just a few of the most common Latin ligatures, and others used in some books I’ve read. (You can also download the document as a PDF.)

GREEK LIGATURES USED IN MANUSCRIPTS
AND EARLY PRINTED BOOKS

This is scanned from John Smith’s Printer’s Grammar, 1755.
Smith classifies the ligatures as: obs[olete], ins[ignificant], orn[amental], conv[enient], and usef[ul].
His comments about the ligatures are included below the chart, and are well worth reading. Those comments should indicate why all of them are totally obsolete today, and were maintained in Smith’s day only by a sort of cultural inertia.