The MOST important thing about how "good" a chord sounds is its context. Wonderful chords played in the wrong place sound wrong. In the "good old days", the following chords lead to the following places:
I -ii, IV, V, vi
ii - V, sometimes I (but pretty much only when the bassline moves from scale degree 1 to 3 or vice versa)
iii - Didn't get used all that much, best handled by professionals
IV - ii, V, I (plagal "amen" cadence)
V - I, IV, vi (deceptive, interrupted or "oh dear, something's wrong" cadence)
vi - ii, IV, V
vii - tricky territory, quite a lot like a V.
Some more options now exist, but it's surprising how much music still follows these rules, thus explaining the ridiculous lack of interest in pop music chord progressions. If you don't know this, it puts it all in perspective:
http://www.youtube.com/watch?v=qHBVnMf2t7w&feature=related It's a I-V-vi-IV, or a "hey, woops, something's wrong, oh, we're in church" progression.
After context, the most important thing is probably voicing, which just means what order the notes come in, and how high or low. This is where the ukulele and re-entrant come into their own, because there is a natural tendency for the ukulele to play fairly "closed" voicings; that is, chords which are crunched together in a tight space. Some complex chords sound great this way.
Beyond that, articulation: how you play it. Strumming a chord might sound rough, but when you arpeggiate it, play all the notes separately, it sounds great. For a ukulele example of this try this Cmaj7 voicing: 4-0-0-3. Terrible strummed, but lovely as an arpeggio.
It's complicated. But that's why we're still finding use for these 12 notes a few centuries after we settled on them.
But he was the kind of teacher where someone would establish a key on the piano as we walked into class, and leave it hanging on a heavy 5th or 7th, and see how long it takes before he can't stand it anymore and resolve it. 
