
Any rating is going to be subjective. Map choice and preparations make apples-to-apples comparisons between classes very difficult. I'm not trying to lay down some kind of absolute truth here, nor am I expecting anyone else to do so. What I am hoping to do is provoke some interesting discussion about strategy and game balance.
I'm going to use a four tier system, just like Darvin did. Top tier are the classes that you would pick if you had to play a game of Desktop Dungeons for your life. They all have powerful and reliable strategies. Bottom tier are the reject classes. They are the ones that just don't work as a character concept. The High and Low tiers are the 'average' classes. The difference between High and Low is a 'soft' difference used to separate very good from the merely good.
I found that the single most important characteristic for me was how reliably a class can confront higher level monsters. Winning out-of-depth fights is the key to efficient play and is vital for the harder dungeons.
Top Tier:
Warlord: He starts with the best glyph in the game, and gets three powers that make that glyph even better.
Berserker: +30% damage when fighting higher level monsters is an incredible power, especially since you should almost either always be either a) fighting higher level monsters or b) one-shotting low level mooks. The magic resistance and +30% damage to magic users are great powers that make it easy to power level off of halpless warlocks and dragons, but I think that the Berserker would be viable even on a magic-free map. The magic penalty is bad without being crippling. You can still pop off a fireball, and you effectively pay a lower cost for following Taurog or using the Mana-to-Health preparation.
Bloodmage: Between BloodToPower, bloodpool, and the supercharged mana potions, you effectively have a gigantic mana pool. In a pinch you can even use bloodpool to support your melee attacks.
Rogue: +50% damage along with first strike means that you can circumvent most of the game. Monsters' attacks and special powers don't mean anything if they don't ever get to use them. The Rogue has powerful synergies with BurnTheirAss, Biceps, and especially Sidestep, and even WaitWhat is pretty good because it short circuits first strikers.
High Tier
Thief: A versatile class that is rarely optimal but never poor. Hoarder means that you get extra powerups, gold, glyphs, potions and sundry items. Survivor means that you get double utility out of your potions as long as you are mixing magic with melee. You can go in blind with a Thief and always find something that will work. This is one of my favorite classes from a design standpoint. It neatly captures the essence of the classic adventure hero, an everyman with no special training or experience but who triumphs in the end due to his clever resourcefulness.
Paladin: HelpMe is a nice glyph that lets melee types efficiently use their mana and also effectively turns poison off. Regaining health for smiting undead is an awesome power that effectively turns all those low level wraiths and zombies into above-average health potions. The 25% physical resistance plays right into the other two powers. It's easy for you to gain health, and harder than normal to lose health, and the two advantages stack multiplicatively .
Sorcerer: A fun class that encourages you mix melee with magic. The +5 mana at start is a huge boost, even better than the Wizard's improved efficiency in most cases. Mana Shield should be seen as a type of melee bonus damage, and mixes nicely with the extra health from Essence Transit.
Low Tier
Priest: People always think of the Priest as an undead killer, but the real action is with his supercharged health potions. The undead damage bonus is just a nice way to gain a few opportunistic level ups. It's no coincidence that the challenge quest for priests isn't a map without undead, but a map where you can't use potions.
Wizard: The Wizard isn''t a bad class, it's just that there are other classes that do his job better. He is the only one of the three 'mage' classes to get a melee penalty (the other two actually have powers that can improve melee). He also gets the weakest of the magical powers. A starting Wizard can cast two fireballs and is 5 mana away from casting three. A Sorcerer starts out with two fireballs and is only 3 mana away from getting a third. A Bloodmage can only cast one, but has a giant pool of mana 'on the map.' The glyph sight power is nice but can be simulated by low level preparations. The extra mana on conversion is a nice power, and will be your primary way of winning the first few out-of-depth battles.
Assassin: With the recent nerfing of IFeelSick, the Assassin lacks a reliable and efficient way to pick on higher level monsters. I came close to putting him in Bottom Tier, but I feel that the Assassin isn't broken as much as not very good.
Bottom Tier
Monk: A melee class with limited physical slots. Resistance is a fantastic power but is hard to capitalize on with such a weak attack. Poison, Weakness, and Corrosion are huge problems with no easy solutions. I think that most problematic issue with the monk is that you can get nearly all of the benefits by playing another class with a Dragon Shield but without any of the crippling drawbacks.
Fighter: Finding equal level monsters isn't as good as it seemed when you were a newbie. The extra experience per fight is nice, but not as nice as consistently fighting above you level. The only power that helps in out-of-depth fights is Pit Dog, but that only works once. It turns out that Death Protection is amazing when it can be cast at will, be is usually only slightly better than having an extra health potion when it's a one-time deal.