Coincidence: I was about to start a thread in general discussions on this very topic.

I purchased a license to Mrs. Eaves almost as soon as it came out, and I haven't regretted it for one second. There are some beautifully inventive ligatures in there (the "g" combinations are wicked!). And it works both in display and text settings.

Cholla Unicase is a fine example of ligatures in a very contemporary setting, and understandably also ships with Just van Rossum's LigatureMaker.

Basically, there is no "complete listing": you can take it as far as you want to. The ct, st, and sp for example are not in use anymore because, due to changing in tastes, most people today find them disruptive in the flow of reading. The sz has been thrown out of modern German, and I haven't seen many examples using the ft and fft-ligatures in Petr van Blokland's Proforma yet.

I'll try to post a couple of examples later on.

Don't forget Eplica
http://www.veer.com/results.asp?image=LFT3020130#about

and Classica
http://www.presencetypo.com/Pages-html/Intclas.html

and previous ligature threads here on Typophile.

Anisette by Jean-Francois Porchez comes with some truely fascinating letterpairings:

http://www.typofonderie.com/Alphabets/Anisette.asp

Good luck

There was a font which won the Carter Prize at the previous Morisawa (not the one that just happened), and it had some amazing ligatures (in fact more like conflations of letters), but I forget what it was called (I don't think it's been released), and don't know where to point to, but I do remember it was by a French designer.

hhp

Also, be sure to include all possible combinations of f and characters with diacritics, e.g. fj, f

Jonathan is right: go over all possibilities with the f overhang and other "clashing characters". For example, what's the use of making fl if you don't include fb, fh etc. Really, now the technical constraints are gone, it's all up to you.

I don't know of a complete listing. I think there isn't yet a
font that explores every ligature possibility.

Mantinia has some nice cap examples.

Mrs. Eaves sports so many ligatures they are housed in
seperate sets and sold with a Ligature Maker app.

And for an unconventional method of connecting letterforms
see the inventive Blue Island.

Most common ligatures (off the top of my head): fl, ff, fi, ffl, ffi

If you want to do something both innovative and functional, make your ligatures based on linguistic frequencies of letter-pairs (or even triplets).

hhp