Many people have already posted on talent specs for 3.1. I wanted to post my own thoughts sooner. Hopefully these thoughts will remain relevant throughout 3.1, so the post isn't immediately out of date!
As priests, we have a few options for our two specs. We can use either or both specs for healing, DPSing, or PvPing. I think it really comes down to personal preference and guild situation whether one chooses to have 2 healing specs, or a healing spec and a PvP spec, or a raid healing spec and a trash DPSing spec, etc. I think I will start out like many priests and pick up a disc and a holy spec for starters, at least until the healers in my guild stabilize and I have a better idea of what's needed.
Here are what I think are the viable/best specs:
Deep Discipline PvE Healing (57/14/0)
In my opinion this is the logical best Disc spec. You get all the goodies, skip the PvP stuff, and get enough in Holy for Inspiration (and Desperate Prayer, a favorite of mine as a Dwarf!) You could make a case for putting 4 more in Holy to pick up Improved Healing, perhaps taking points from Focused Will or Improved Flash Heal, but I don't think it'd be worth it, with Penance's cheap cost. It depends on the frequency of casting Greater Heal as Disc.
Deep Holy PvE Healing (14/51/0 + 6)
This is the skeleton of most deep Holy builds, I think, covering all the essentials and leaving 6 points to place where you like. Circle of Healing and all the talents that help it, the staples Holy Concentration and Surge of Light, and all the passive healing boosts for big throughput. With the remaining points you can choose to also have a better Renew in your arsenal, the passive Test of Faith for healing where it counts, Serendipity for faster Greater Heals, or better efficiency from Mental Agility in Disc. You could shave a few more points off of say blessed Resilience or others too, depending on taste.
Holy/Disc PvE Healing (21/60/0)
I cooked up this odd spec, squeezing the Disc talent Soul Warding into a CoH build, and I'm not sure if it's any good. I thought of it because I think PW:Shield is underused by Holy priests as well as Disc ones, and Soul Warding would let you through out a couple of shields in between CoH cooldowns. Without Disc's massive shield buffs, it may not be worth it, but it could be interesting for dangerous trash packs, or perhaps for some gimmick encounter.
The idea of a LolSmite spec has a soft spot for me, and with dual specs you can always get a wacky spec for your off spec. Surge of Smite is probably not going to top a raid damage meter but it can do decent DPS if you're looking for something fun to try. For more info I have to recommend Xel's new smite DPS blog.
Of course, Shadow is the traditional DPS spec, and comes with excellent trash-pack APE damage in Mind Sear, so it can be a good secondary spec for clearing trash. WoW Insider had a great post on shadow specs the other day.
PvP Healing or DPS
I'm afraid I haven't kept up with PvP in WotLK, and I don't want to post a PvP spec without any experience. I would imagine that deep Disc is the preferred arena spec for its enhanced survivability and shielding, but that deep Holy has potential especially in battlegrounds. The new talent Body and Soul seems very nice for the BG involving flags and quick travel.
Hopefully this spec advice is sound and helpful. Time will tell, as we advance through Ulduar, which specs are best for the encounters there. Have fun choosing a spec and switching between specs!