Priests are one of the most versatile classes in World of Warcraft and with their three different trees comes a variation of viable specs that can accomplish different things. Here are some specs that I have used in the past that are viable and could be used depending on your own personal play style. There is no necessarily "wrong" spec to have as long as you can justify using it. Take note of your own spell usage (ie do you use Renew a lot? Flash Heal? PoH?) and alter your talents accordingly.
Special notes: For all three trees, at least 13 points in discipline is required. Meditation is pretty much a no-brainer, as are Improved Inner Fire and Improved Power Word: Fortitude to get there. Twin Disciplines is pretty much mandatory as well for first tier, unless you are putting together a pvp spec. For healing, Inner Focus is generally taken just because it is so powerful with Divine Hymn, and a free spell every three minutes can help a lot.
HolyRenew oriented raid healing spec:
This is the spec I currently use. (However, I'm planning on shifting some points to Body and Soul to play with it during raids.) It can be a controversial spec and relies heavily on the priest's usage of Renew. This spec shines on fights where there is constant raid damage, such as Twin Valkyr (in which HPS can really skyrocket). However, be warned that this spec is not for single target healing or even burst healing and thus should not be used on fights that require such (and even 10 mans will expose the weakness of this spec). This spec's spell usage generally sees spamming of renew on any player that will need healing and relies on a constant stream of healing. On fights like Twin Valkyr, general spell rotation will be something along the lines of: Prayer of Mending, Circle of Healing, Renew, Renew, Prayer of Mending, Circle of Healing, Renew, Renew, repeat. This spec also allows the priest to pull out hasted Prayer of Healings when the time comes, though somewhat infrequently as the only source of Serendipity will be Surge of Light procs. Greater Heal usage should be nonexistent - Spell Warding is taken instead of Divine Fury for personal survival and with no points in Empowered Healing there will be little force behind the heal. Flash Heal should only be used with Surge of Light or spot heals here and there as Empowered Healing will not contribute to that either.
Suggested glyphs: Renew, Prayer of Healing, Circle of Healing
Flash Heal oriented:
As you can see, there is little variation from the previous spec. No points in Blessed Resilience and only 1/3 in Empowered Renew put into Empowered Healing (5/5) will really strengthen flash heals so that will be your bread and butter in this spec. Renew should be used as a filler at best - 1/3 in the talent is to allow the instant healing to take place and thus cause surge of light procs. No Blesssed Resilience means 3% less on the rest of your healing spells so use Flash Heal much more liberally. However with this spec Serendipity should be up a lot and thus Prayer of Healing will be getting a lot more usage.
Suggested glyphs: Prayer of Healing, Circle of Healing, Flash Heal/Guardian Spirit (Depending on if you have mana issues)
HOT Based:
For those who love to play like resto druids. It is a stronger variation of the Renew spec but should only be used if you are absolutely positive you won't be using Prayer of Healing. Mental Agility will allow you to spam Circle of Healing, Renew, and Prayer of Mending all for a bit longer. You also lose one point in Surge of Light but your crit should be high enough to still proc often enough. Surge of Light procs also become less important since you are no longer proccing Serendipity. The problem with this spec is that outside of Inner Focus+Divine Hymn, you don't really have any big burst heals. That being said, it'll be up to you in order to be casting pre-emptively enough to ensure that you're never in a situation where the use of Prayer of Healing would outshine your ticking HOTs. (Note: If you aren't having mana problems, you can drop 2/2 Healing Prayers for Body and Soul to play with.)
Suggest glyphs: Circle of Healing, Renew, Guardian Spirit
*Note that none of the specs takes Divine Fury. There are still priests who think that Greater Heal is a useful spell and far be it from me to argue the usefulness of it but at this stage in the game, the cast time is far too great for such little reward. There is some viability in a spec with 5/5 Divine Fury and 5/5 Empowered Healing that could take advantage of Serendipity procs to get a fast Greater Heal, but it just isn't as efficient any more. Plus, Greater Healing takes the most talents to buff - Empowered Healing, Improved Healing, and Divine Fury: 13 points total. In my personal experience, I have not used Greater Heal more than a couple times a fight, so those points are really just being wasted. Holy is more or less the raid healing spec now so there shouldn't be much need for large single target heals. Disc is a better alternative.
Discipline"Cookie-cutter":
The holy points are more or less debatable but you should drop points to get to Inspiration and really the last point is only useful in Desperate Prayer (which can still be lifesaving in a number of situations). You can choose to drop points from Spell Warding into Divine Fury if you want to pull off some hasted Greater Heals from Borrowed Time or sacrifice some crit to max it out, but the scaling of Greater Heal for disc is even more abysmal than holy so I would not recommend this. With the discipline tree there is little variation you can make - most of the talents at the bottom are mandatory to make up for the lack of any stat conversion to spellpower. Discipline itself is a strong raid mitigator now - stack spellpower and spam Power Word: Shield. With enough spellpower, your Power Word: Shield becomes a 6k~ instant heal that is spammable. Use it. Be aggressive with it. There are many fights where you can exploit the crap out of the mechanics of Rapture if you are having mana issues (which you should be, because spamming PWS aggressively can hurt your mana). Penance is best for support tank healing - the longer cooldown has drastically cut down single target HPS. Flash Heal is useful when you are spot raid healing (perhaps when the raid member has Weakened Soul) due to the crit on low health members but it will probably not be enough to keep a tank up between Penance cooldowns. Don't try to be a hero - get another healer (preferably a paladin) to cover your tank as well. You are now a variation of raid healing (er, raid bubbling) with a fantastic ability to support a main tank healer. (Generally in raids, I PWS spam and then Penance whichever tank is the lowest. Then flash or PWS until Penance is up again.) Remember to use Pain Suppression on cooldown unless you are saving it for a particular ability. Use Power Infusion on whoever is most beneficial for the fight - a DPS (who benefits from haste, say Art) if it is a DPS check and we are lacking or a healer (generally a paladin, say Kadas) if the healing is going to be intensive.
Do not waste your global cooldown by casting Renew. Make sure your healing addon has the ability to show who has Weakened Soul so you aren't wasting time trying to bubble someone who can't be bubbled and you know when they can be bubbled again. Tanks, for instance, should always have Weakened Soul.
Suggested glyphs: Flash Heal, Penance, Power Word: Shield
Shadow"Cookie-cutter":
Meditation is mandatory yet Inner Focus is not unless you have taken points from shadow and don't have anywhere to put that last point. Inner Focus is currently bugged in that if it does not increase the critical chance of a dot - when it is fixed it will probably be beneficial to pick it up and use it with Shadow Word: Pain right off the bat. This shadow spec is built for the most DPS but you can alter it according to your gear and/or the encounter. Improved Vampiric Embrace can be really useful on certain fights where there is a lot of raid damage and you want to help the healers out. Shadow Affinity can also be extremely useful on fights where you are going to have aggro issues - Hodir for example. With 3/3 in Shadow Affinity you can never really pull threat, even with Vampiric Embrace healing you. If you really want points in these talents, I'd suggest taking points out of Focused Mind or Shadow Focus if you can sustain your mana. Shadow Focus can be played with since there is just an obscene amount of hit on our gear nowadays so you may find yourself way over the hit cap and thus could take a point out.
Suggested glyphs: Shadow, Mind Flay, Dispersion or Shadow Word: Pain
Mana Intensive:
This spec is for shadow priests who can manage their cooldowns well to avoid running out of mana without Focused Mind. You gain Improved Vampiric Embrace (which can improve your unique utility and be very helpful in many fights) as well as Inner Focus. Inner Focus is still bugged to the point where it can't affect a DOT, but you can keep it in your hat for an emergency Divine Hymn if it is needed. If you are very, very confident in your healers, you can use it in conjunction with a Devouring Plague to help out on mana. You'll have to try to pop your fiend at least twice a fight - sending it out when you're at 70-80% mana is a good idea so it'll be up again. If you can send it out with Heroism, that is also very beneficial. Glyph of Dispersion is really the only choice here - Shadow Word: Pain does not offer much in mana return and if you can time your Dispersions well as to not lose DPS time, you can gain a lot of mana back.
Suggested glyphs: Shadow, Mind Flay, Dispersion