All these builds are very tweakable, and are not intended to be the end-all of talent specs. Feel free to adjust them how you see fit. However, like the rest of the info on this site, I hope it will be a solid foundation you can build off of.
These are basic builds you'll see recommended on the forums. Whenever someone says "You should go a x/x/x build", chances are they're talking about something similar to the below.
The goal of this build is to have a lot of instant damage, and a lot of versatility. You have powerful frost defenses with Ice Barrier, Ice Block, and Ice Floes to keep them handy. You have powerful Fire offense with Ignite, 3/5 Fire Power, and Improved Fire Blast. You also get nasty ice lances and CoCs from frost, and Blazing Speed is absolutely amazing against warriors, rogues, and especially hunters. The problem with this build is it's very mana hungry, so it won't last very long in arenas or in prolonged fights. It's also awful for PvE, as you don't really have a "go to" nuke. You could replace Burning Soul and Master of Elements with Improved Scorch to make it more viable in PvE (and give you a debuff to annoy paladins in PvP).
This is very arguable. For example, you could put points into Improved Arcane Missiles instead of subtlety and focus (especially fun with a Mystical Skyfire Diamond), giving you a goto finisher when you have a hunter pet on you. I left out Empowered Frostbolt, since generally a lot of your damage comes from other spells with this build in normal PvP situations. If you find yourself frostbolting more than me, though, that's certainly a solid talent. Arctic Winds is also a contender. This is a build that can also do well in PvE, though it won't be topping the damage charts. Solid (and popular) arena spec.
This build is built around solid survivability with nasty burst damage. Yes, that's Arcane Fortitude. Yes, you can get rid of it, but I needed a point somewhere and there it goes (and every bit of defense doesn't hurt). Improved Blink is actually a very solid talent, and I miss it after speccing out of it. Your mana pool will last a while with this build, and with AP you can dish out the pain in a hurry. If you can't stand controlling your water elemental, this is the frost spec for you. Just remember that an AP fireball will still outdamage an AP frostbolt (even with Shatter, the fireball's crit damgae is barely behind the frostbolt's and the normal damage is much, much higher), so tune your macros accordingly. This is also a solid arena spec.
A fun arena spec (with Impact for Molten Armor), this is for you true frost lovers. You lose out on Improved Counterspell from the 17/0/44 build, but you gain a lot more frost damage and more solid defense. It'll work in PvE as well. A popular variation is going 0/7/54 to pick up Flame Throwing as well.
Don't use this in arenas, but if you like burning things, this will light you up (HAR HAR). Improved Counterspell through Arcane will help out with casters, and the rest is focused on burn, burn, burn. Fireball is totally avoided in favor of Scorch and Fire Blast. Scorch when you can, Fire Blast and Blastwave when you can't. Dragon's Breath makes a great control tool for an otherwise defenseless tree, and Blazing Speed will help you out of tight spots. Fun in BGs, but you won't survive long if you're focused on.
This was the build I used in I Suck At PvP, which takes out Empowered Frostbolt to pick up a faster Fire Blast and Burning Soul. The idea behind Burning Soul is that it gives you a "go to" spell (Scorch) that's efficient and relatively nice DPS even without fire talents for when your instants are on cooldown or you're getting low on mana. The 70% anti-interruption ability makes it GREAT against other mages (especially with a WE pelting you), warlocks (just ignore the pet and keep nuking between instant CDs), and hunters (though you should rarely stop to cast anyway). The passing of Ignite was intentional to make it so that Molten Armor crits wouldn't break Polymorphs. My reasoning for passing Empowered Frostbolt was that with my current playstyle, I wasn't actually casting Frostbolt all that much and I didn't have a ton of +damage to really take advantage of it. Honestly, I now feel that this was a mistake, and don't really recommend passing up this talent unless you have 500 +damage or less to start with. Still, the build was a blast to play and I highly recommend it to at least try.