If I'm going to break down every class I'll take it from the pve side, and judge them in 3 categories: solo, 5 man, and raids.
Shaman: lots of versatility in this class, and after 2.3 they can solo with enhance and actually use some shocks now. Which means it's no longer auto-attack + stormstrike when it's off cooldown. Their class defining system, though (totems) is useless while soloing unless you aggro a large group, or if you're soloing an elite. At 70, if you are elemental/resto spec and geared out, you can also kick ass while soloing quite easily, though elemental can be tough unless you invest in the eye of the storm talent, which is seriously more of a pvp talent. Grouping, each spec can get by easily. This is where you use totems, and enhance also buffs the group by meleeing. Elemental doesn't bring any specific buffs from dpsing, which sucks, but it does provide pretty consistent caster dps. Resto is a great healer that requires a lot of mana per 5 seconds gear to sustain its mp, although 2.3.2 makes a huge stride for this with the new water shield. In raids, all 3 specs are also equally appreciated (or should be, anyway) though I would say that resto has the edge in a 10 man raid since other dps/caster classes have more utility.
Solo: B+
5 man: B
Raid: B+
Paladin: by far the best, and biggest range, of buffs in the game, so they can benefit any group pretty easily. Solo is annoying unless you spec ret/prot and twink out with some great gear. For 5 mans, you are pretty indispensable because of your buffs, and you can heal/tank pretty effectively based upon your spec. Raiding is maybe the weakest link for paladins as a healer, because they only have direct heals, although they also have super strong and efficient heals, so they're an excellent tank healer. They're also an excellent tank, especially on fights where you need someone to hold multiple mobs.
Solo: D
5 man: A+
Raid: A-
Druid: solo is easy with this class if you are feral or balance. Balance is an underlooked spec, even by blizzard themselves (seriously, you have to poach from warlock/mage cloth, tailoring, or get a set from badges/raids to get caster gear for the most part) but it also excels at soloing. It can be tedious compared to feral, since you essentially moonfire, root, and starfire/wrath your enemies to death, but arcane/nature immune are the least encountered mobs in the game (rock elementals are immune to nature and that's about all I can think of) and when you do run into something that's nature immune, you can always switch to arcane. Feral solo is awesome, but don't expect it to be just like a warrior/rogue. you do good dps, but in my experience a lot of it is more sustained and with less big crits. In 5 mans, a druid is surprisingly awesome. They can tank easily with feral spec and bear gear, dps, and heal. Balance is one of the more hated specs for 5 manning, yet ironically it's a very good heal spec due to the regen talent, int->damage/healing talent, and being able to go 5/5 imp. MotW and 3/3 intensity out of resto and stack even more regen, plus still having innervate. Raiding makes each spec viable, just like with shamans, though I would argue that balance probably gets the shaft in 10 man raids compared to 25 mans. Balance/feral specs' auras really make them beneficial in raids since you can configure groups to make them even stronger.
Solo: A+ (grinding can be slow sometimes, but they are gods of solo on par with hunter/warlock)
5 man: B
Raid: A- (tanking is their one weakness in raids since there aren't a lot of good feral tank drops from raids, but this is where you put them in a dps group with rogues and an enhance shaman to provide damage support)
Priest: Shadow is the most preferred solo spec because it's easy to get, but people have discovered some decent holy/disc leveling builds as well. The benefit of those builds is there is no holy resist, and obviously they won't be cut off from healing spells, so they can pop into instances while grinding and heal away. That build probably requires a bit of twinkage, though, and I'd still say it needs 5 points into spirit tap. Anyway, solo is something they get better and better at as they go along. Healing is where they're the strangest - they have, by far, the best selection of healing spells since they have a heal for every situation, but they're jack of all trades, master of none. Most people don't even want holy/disc priests on raids anymore compared to shadow, but if a guild needs healers they won't turn down a healing priest... truthfully, I think blizzard made shadow have so much group utility because they wanted all the priests who spent ages before TBC doing nothing but healing to have the option to do something else, since healing is by far the least fun job I have done in WoW. Anyway, their two specs are great for raiding. Either they have versatile heals, or they have versatile dps that keeps a group's mana up, which makes them great for a healer group especially. I think this class's dps potential with shadow really comes into play in raiding.
Solo: C+ (definitely not their strong suit, though from 40+ on they are very, very good soloers with shadow talents)
5 man: B+
Raid: B-
Warrior: these guys kick ass if you spec them for dps, which you should do until 70 (and even after then, but what I mean is if you really want to be a prot tank, don't bother until 70). Solo, they can chew up mobs one after the other, and just get better as they get higher level and get better gear. They do require pretty hefty gear maintenance/upgrading to stay sharp, but that's why you run instances. 5 mans, they tank and that's it. A warrior dpsing in a 5 man is very, very rare - at least in the sense of just being there for dps. A dps warrior tanking a 5 man is very, very common - all they need is a good set of tank gear and they can handle any 5 man you throw at them for the most part. Definitely the most equipped tank in terms of abilities. The bulk of their skills honestly are related to tanking, but they pick up kickass dps skills along either the arms or fury tree. Raiding is where a warrior can get the option to dps/offtank, sometimes doing pure dps (though probably less with the 25 man raids in TBC). In this case, they have blood frenzy to buff everyone else's physical damage, which gives them some nice utility to go along with their awesome dps.
Solo: A- (only falls behind the druid, warlock and hunter IMO, but prot spec would be the same as a pally or worse)
5 man: B+ (only knocked down from an A because there's very little opportunity for a warrior to go pure dps in a 5 man)
Raid: A- (either a tank for nearly any situation, or a dpser who indirectly buffs your raid's dps)
Rogue: it's going to be straight-up dps with this class no matter what. Solo, they're pretty good killers who get better as they get better gear, just like a warrior. Stealth lets them skip a lot of content, which is nice. Pickpocketing can earn little bits of extra cash or potions. Poisons are pretty nice now that they don't have charges, although having to level up the poison skill like a profession is annoying. In 5 mans, they bring sap for some CC, stuns, and their poisons may get a bit more work. Raids are more of the same, though at least pre-TBC most raid mobs were immune to stuns/sap. They provide some reliable low-threat dps. My one big gripe with the class is the energy cost of their skills - with how many strides blizzard has made to make mana regen better for casters, and the low rage cost for similar dps output to rogue skills, it feels like the energy cost for a lot of their attacks is too high. White damage makes up most of their dps anyway, but I still think blizzard could do something to balance rogue skill costs, or energy regen or something.
Solo: B
5 man: B+
Raid: B-
Mage: I like their dps, but I find the class pretty boring to play, personally. They stand there and nuke... that's about it. Low health makes them annoying to solo with until you're a higher level, since they drop pretty fast. Mana regen can be annoying, you never have to pay for food/water and you can conjure your own mana potions (basically) on their own timer, so at least downtime costs nothing and you can sometimes end it quickly. They have an easy to use CC spell with polymorph, which handles the majority of instance/grinding mobs, but is more useful while soloing as something to pull a pair of mobs with than something to use mid-combat since it will only buy you time for mana regen or an easy escape. In 5 mans/raids you have someone else to take the hits for you, so your nuking can really take off, but again you usually have to drink at the end of a fight. Plus you're expected to give everyone food/water, which can be annoying (especially when a hunter harasses you for a stack of food for their pet). Teleports cut down your travel time, and you can sell the shattrath portal to lowbies in Org/UC for the horde, or Candyland for the alliance. A decent soloer because of raw dps, but truly shines in groups where they only have to watch their aggro and their sheep.
Solo: B-
5 man: A (I would take a mage on just about any 5 man in the game, even if it doesn't have anything they can sheep)
Raids: A- (mana regen can be a problem for them, but they still provide some powerful dps and satisfying big numbers on spell crits)
Hunter: probably the most mind-numbing class I have soloed with, yet amazingly fun in groups, and equally awesome at both. They start out weak until level 10, then they get their pet and don't look back. The only drawback is giving up a bag space for a quiver/ammo bag. Great utility in groups in the form of a pet offtank on weaker mobs, freeze trap to CC anything and excellent sustainable high dps and easy threat management. I don't know what hunters really bring to raids in TBC, but pre-TBC it was essentially good dps, tranq shot, and little/no threat.
Solo: A+
5 man: A-
Raids: C+ (their big weakness, probably)
Warlock: everybody hates warlocks unless they play one, saying they are easy mode, etc. but they have some challenge to them. They are awesome soloers and have a lot of group utility, but they take time to really get strong. TBC put them on another level, which is fine because it essentially made them feel much more complete than they did pre-TBC (where they were fun, but still felt like half-assed mages with pets and a taxi service for fucktards). Unlike hunters, they are awesome in raids. Unlike mages, they get tons more HP and good ways to replenish it, and never have to worry about their mana. What used to feel like a shitty cross between a hunter and a mage is now a pretty awesome class that meets them in the middle and then smashes their heads together like Moe in the Three Stooges.
Solo: A+
5 man: A
Raids: A
I should close this by again stating that I'm only ranking them on pve. I have like no experience with arena in WoW, and honestly don't even have that much TBC raid experience, but I know they didn't change up that much of the classes (aside from priests, shamans and druids anyway) for the raid game. pvp is a totally different animal, even if it works under like 95% of the same rules as pve does, so I'll leave that to someone else to decide.