Desperate Prayer: Instantly heals the Priest, with no mana cost, on a 10-minute cooldown. Available to Humans and Dwarves starting at level 10.
An excellent skill for solo and group PvE as well as PvP. Who, after all, can say no to a mana-free heal? Through the levels, it's about as effective as a Flash Heal. And its relatively short cooldown means that it's usually available to use when you need it.
WoW Insider rates this ability an A+. Useful in all situations you might find yourself and can make the difference between life and death for both you and your group (as your group isn't likely to survive if you find yourself dead).
Hex of Weakness: Reduces physical damage done by your target and reduces the effectiveness of healing on that target by 20%. Available to Trolls starting at level 10.
HoW isn't a great skill, but it has its uses. In a group or raid situation, it's always helpful to have less damage hitting your main tank. In PvP, it doesn't hurt to reduce healing effects on a target, if they have dedicated healing on their side -- and reducing damage by 35 may not seem like much, but it does add up over time.
WoW Insider rates this ability a B+. It can be handy in nearly every situation you find yourself in (so long as you remember to cast it!) -- it's a minor effect, but its impact adds up over time.
Starshards: A channeled spell doing damage over time to your target. Available to Night Elves starting at level 10.
A handy spell for leveling up, especially if you aren't speccing Shadow. It's decent damage and can take the place of Mind Flay in a DPS rotation. But if you're speccing Shadow, you're probably going to be using Mind Flay instead.
WoW Insider rates this ability a B-. It can be useful while you're leveling, at least if you're trying to level with an unfriendly leveling spec.
Symbol of Hope: Regenerates mana for members of the Priest's party over 15 seconds on a 5-minute cooldown. Available to Draenei starting at level 10.
A great skill for all times and places. Any form of mana regeneration is highly desirable, and having an ability that regenerates mana not only for themselves, but also for the rest of their party, is extremely handy, especially for late game instances and raids.
WoW Insider rates this ability an A. Useful for end-game raids and instances, where the mana it restored can make a difference for the better. However, less useful in PvP, where you're likely to end up dead before you end up out of mana, and leveling, where you usually have plenty of time to regenerate mana by drinking between pulls.
Touch of Weakness: Does damage to and reduces the damage caused by anyone who hits the Priest while the buff is active. Available to Undead and Blood Elves starting at level 10.
WoW Insider gives this ability a B-. Handy for leveling and PvP, and the damage reduction can be the difference between life and death in some situations. (35 less damage per hit doesn't seem like a lot, but it adds up.) However, the fact that the target has to hit you before it does anything makes it nearly useless for groups and raids.
Consume Magic: Dispels one beneficial effect on the priest in exchange for restoring mana on a 2-minute cooldown. Available to Blood Elves starting at level 20.
Restoring mana is always helpful, but in the case of Consume Magic, it comes at a fairly high cost. When you use it, it dispels one Priest buff from you at random. This could be a cheap cast like Inner Fire (375 mana per cast at level 70) or it could be an expensive cast like Power Word: Fortitude (2080 mana per cast at level 70) for a mana restore of 453 to 488 (again, at level 70).
WoW Insider gives this ability a C. The restored mana can be useful, and it could even make the difference between a wipe and a successful pull. However, you don't now what it will take from you when you cast it -- it could be something you need. And the mana it restores simply isn't terribly overwhelming compared to the mana cost of the buffs it could dispel.
Devouring Plague: A shadow damage DoT that heals the Priest for the damage it deals. Available to Undead starting at level 20.
Excellent spell for leveling or PvP. Not only does it do damage, but it also heals you. Not hugely useful for late game groups and raids, however, since healing duties will often prevent you from having the time or mana to use it. (But great for a Shadow-specced raider!)
WoW Insider gives this ability an A. Excellent utility in a variety of situations, though as with most damage spells, it might not find space on your toolbar
Elune's Grace: Temporarily reduces ranged damage taken and increases dodge chance on a 5-minute cooldown. Available to Night Elves starting at level 20.
Extremely situational and it doesn't last long enough to be overwhelmingly useful when you have a situation where you might need it. Essentially, you can reduce ranged damage taken and increase dodge chance for 15 seconds out of every 300 seconds.
WoW Insider gives this ability a C-. The buff it gives is highly situational, and in situations where it might be helpful, it doesn't last long enough to make much difference. Perhaps worth casting on the main tank in an instance or casting in PvP when fighting Hunters.
Fear Ward: Protects the target from a single Fear effect, on a 30-second cooldown. (The first Fear that hits the target will remove the buff, but not fear the target.) Available to Dwarves and Draenei starting at level 20.
This ability is incredibly useful in certain group and raid situations that use Fear as a key part of the encounter. While there aren't any encounters in the game that are impossible without Fear Ward, having Fear Ward can make these encounters trivial. Also has use in PvP, where fear is so often used.
WoW Insider gives this ability an A. Many players would call this the best ability for a priest to have -- and plenty of Priests have been allowed or declined entrance to raids based on having or not having it. However, we're only giving it an A because -- while it's incredibly useful when it's useful, it's still situationally useful.
Feedback: A buff that burns the mana of anyone who hits the Priest with a spell, doing shadow damage for each point of mana burned. Lasts for 15 seconds on a 3-minute cooldown. Available to Humans starting at level 20.
At level 70, for a cost of 705 mana, you can burn 165 mana and do 165 damage to your target. There is no situation in which the mana used is worth the amount of mana burned or damage done. In group situations, this skill is essentially useless, as in a perfect world, a Priest in a group shouldn't be taking hits.
WoW Insider gives this ability an F. It's hard to see why anyone would bother training this skill, much less keep it on their hotbar. Even at a time when you happen to be fighting spellcasters, the spell costs a good chunk of mana for a small amount of damage done and mana drained.
So what's the final story? I think looking over this list it's impossible to say all of these skills are of equal use. But how's Blizzard to fix things? The only way to make things 100% equitable for all races of Priest would be to do the same thing Blizzard did with Shamans and Paladins -- where Shamans and Paladins are now open to both factions, giving racial skills to all Priests would stop all arguments of balance. (Though that would give them quite a pile of extra skills.) However, Blizzard has held on to the idea of unique racial abilities since the game's launch, and it seems unlikely, at this point, that they'll give up on the idea. So... for now, if you're planning on starting a Priest character, pay close attention to your race -- some are undoubtedly better than others.