Wow, you dug up a really, really old thread, lol.
I've learned a lot since this, so let me throw this out there real quick:
Clan boss - Ideally, you want a lifesteal set and speed set. If you are running a counter group and can get up to the minimum speed for your respective boss (171 for NM or 191 for UNM) without a speed set, then you can load up on more defense with a defense set, more hp with an immortal set, or otherwise have more options depending on that champion. Some people even go with a crit rate or crit damage set along with it, as those will help you heal with lifesteal anyway. But, lifesteal is a staple in any group. Once you combine it with warmaster or giant slayer, it's just way, way too valuable for topping off your HP. You don't even need a healer with it.
Arena - If you want to get in gold IV, you ideally want a speed team. One champion should have a speed aura, and you need someone on the team that has a turn-meter boost to get everyone else a turn before the enemy. I can tell you from personal experience, when I went from a glass cannon team with atk % aura, to a speed aura with High Khatun, I went from a low gold team (gold I), to gold IV immediately. Speed always has the upper hand. Once you do have that, like Erikbogart said, you have more choices. Frost on a champion you know they will target, like your healer or ressurection champion (like say Gorgorath) can be great. Otherwise, I suggest glass cannons to kill, modest accuracy on your debuffers (def down, atk down, provoke, etc.), and speed. My videos from when I changed up speak for themselves. Just watch the ones where I still had Inithwe in them (atk % aura) to the ones with Khatun in them (speed aura). It was a world of difference.
Dungeons - This is where things get a lot more complicated. The ideal sets in here will really depend on the champion and the respective dungeon. Depending on the champion and your team composition, quite a few sets could be good. Let me just name them off here:
life set - inferior to immortal and divine life. only choose life over one of those two if the other stats are much better
offense set - again, inferior to cruel and divine offense. only choose if the stats are much better. also, crit rate and crit damage are FAR more valuable in this game than raw atk
defense - viable
critical rate - viable
accuracy - viable
speed - viable
resistance - rarely viable. sometimes useful on your lead champion (tank) on Spider dungeon, but usually not very good unless you have a champion with a strong taunt or otherwise getting attacked more than any of the other champions
crit damage - viable
lifesteal - viable anywhere. again, once you have warmaster and giant slayer, this is a great set. the only exception to this is if you have a healer or other type of champion who has lots of skills that don't tend to attack or otherwise damage the enemy. if you aren't attacking much, obviously this set won't do much good.
destroy - complete garbage. NEVER useful anywhere. the numbers just aren't significant enough.
retaliation - VERY rarely useful, unless the champion has an AMAZING A1 and/or is a tank that gets targetted a lot and it would be reliable. Someone like Bad-El-Kazar could use this with great efficiency in dungeons, but there are few champions where this is viable
fury - RARELY ever viable. it would have to be VERY situational to make it worth it, as it is inferior to crit rate or crit damage, which aren't dependent on you losing life. Only champion I am thinking of that it could even be remotely useful is Skullcrown, but even then, I believe other sets would be preferable. *Might* be useful on her in arena on a defensive team, but I discourage defense teams, so I really just don't suggest it.
curing - complete garbage
reflex - rarely useful, unless the champion has ridiculously powerful cooldowns, like maybe Roshcard or some other OP champion. it's too unreliable at only 30% and with a *random* skill, so might not even reduce the one you want
cursed - VERY situational. if you have a solid team for say Fire Knight Castle, but no one on that team that prevents healing, then this could be a solution. otherwise, it's just not very good.
toxic - complete trash. 2.5% poisons are just way too weak. they take up a slot that a 5% poison could.
frost - as erikb already stated, can sometimes be useful in arena with a defense team, or possibly in dungeons where you have a champion with provoke or otherwise tanking the dungeon. But again, I do NOT support defense teams in arena personally, so really just for a select few dungeons with the right champions that you KNOW will be getting attacked over your other champions.
daze - garbage, since as soon as the target takes damage again, the debuff is removed
immunity - garbage. this would again be useful for an arena defense team, but once again, i do NOT advise defense teams over speed teams. in dungeons, your teams *should* be so much faster than the enemy that it will most likely drop off before it ever even serves its purpose. *maybe* if it lasted like say 4 turns, but then it would be VERY OP in arena
avenging - retaliation is FAR superior to this. garbage set
shield - garbage. again, only use would be on an arena defense team
stalwart - garbage
frenzy - garbage
regeneration - inferior to immortal. unless the stats are amazing on it, it's trash
stun set - useful for champions with LOTS of AoE attacks, like possibly on Bellower, Psylar, or someone like that
relentless - inferior to a speed set and too unreliable. only use it for long-term encounters, where you have better odds of it occurring, and only if the stats are MUCH better than your speed sets
savage - this could be good on your high damage dealers, but I am unsure if it is up to par with cruel sets or not. have yet to do the calculations on it, as i have never farmed for it (I tend to farm dragon dungeon, as the overall sets there tend to be more useful for me)
taunting - rarely useful. at 30%, too unreliable. unsure though if the taunt is attack based, or hit based, meaning if your champion has a 4-hit A1, if that would be four 30% changes, or just 30% for the attack itself. either way, still too unreliable to be viable, save for *possibly* some very rare situations where you need that champion to tank as much as possible
cruel - GREAT set. other than your speed aura and turn meter booster in arena, this is the MOST valuable set in arena, at least on most champions. with 3 cruel sets, you ignore 15% of the enemy's defense, PLUS you also have that extra 15% attack on top of it. only others that could potentially be better would be crit rate or crit damage sets, depending on the stats on the artifacts
immortal - GREAT set for HP or defensive champions. with a full 3 sets, that's 9% HP healing every round on top of the extra 45% HP the sets would offer. great for champions whose healing is based off their HPs, like say Pain Keeper (although after the nerf in 1.8, she is fairly worthless in end-game content, save for with champions with EXTREMELY powerful cooldowns. even then, she is unreliable, as you can't count on her casting A3 at the ideal time when it comes to auto-farming)
divine life - better than a life set, inferior to an immortal set. only exception would be an arena defense team, but you already know how I feel about them.
divine crit rate - better than regular crit rate, depending on the stats on it. unless the stats are better than on crit rate, I wouldn't suggest it
divine speed - better than regular speed, with ONE exception - if your masteries include the support tier with the added stat bonus from "lore of steel", then unless the stat bonuses on this are better than a speed set, prioritize speed sets
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Two things to add here...
1) Prioritizing a set over the stats on the gear is not always the best decision. For instance, if you need crit rate, but a frost piece and a cruel piece combined offer 35% crit rate between the two, and you have a crit rate set that only have 13% combined on them, then it would be better to choose the two that are not part of the set, as even with the set bonus, the crit rate set would only offer 25% compared to that 35%. So, if you have an off set that has some REALLY amazing stats, might want to do a basic number crunch.
2) If an artifact has the stats you need on it, I typically suggest you level the gear up to level 8 and see which stats increase. While the base stat on one artifact may be higher than the base stat on another one, until you start leveling it up, you don't know for sure which stats are going to get the 4, 8, 12, and 16 set bonuses. Leveling gear to 8 is fairly affordable, MUCH cheaper than going to 12, and gives you a better idea of how good that gear will be compared to others.