I collected some games where I used Transmute to good effect
here, and another one
here as well.
I buy it a full 22 percent of the time, and win just as often as I lose with it. The best, and easiest to figure, situation for Transmute is games which have A) Curse-givers, B) other Potion cards, and C) no other trashing. It is sometimes worth it if only two of those three conditions are met, but that's much less of a sure thing. No other trashing is the real key, here, since Transmute does have such a high opportunity cost compared to any other trasher. Curse games are also key, because they drag things out long enough that Transmute's extreme slowness is mitigated; ideally the Mute will clear a bunch of Curses and turn at least two of your Estates to Gold.
Once in a rare while it might be possible to use Transmute's other options to power Vineyards, Scrying Pools, or Dukes, but these situations are really rare. Late game Action->Duchy moves for tiebreaker points are more common, but still not something you can really rely on.
Basically, Transmute is something you want in Familiar games, and not much more often than that- but probably more often than you think.
...
In addition to the several games I collected in the links above, here's a few more cases where the 'Mute was useful:
http://councilroom.com/game?game_id=game-20120110-101623-aa27df75.html Ambassador here functions as a stand-in for game-slowing Curse cards. Obviously Transmute was a very small part of the game plan here: but it gets me all my Gold, a Duchy on the last turn, and ups the chance of Menagerie hitting. Probably wasn't actually necessary, but I found it useful.
http://councilroom.com/game?game_id=game-20110927-163154-b9357611.html Picked it up as a consolation prize instead of Scrying Pool on an unlucky $1P hand early, and it just did the Estate-to-Gold thing three times. Had there been +Buy here, mass Transmute contagion into Vineyards would have been strong.
http://councilroom.com/game?game_id=game-20120213-111046-b75f547c.html When there's a potential Goons engine to be built, yes it can be worth buying that Potion to buy that Transmute just to clear Curses. Yes really.