What To Wear for Cold Weather Running?

Since the weather is about zero degrees with a chance of blizzard here, "what the hell do I wear?" seems like a good question to answer.

Upper body
Sports bra (for the ladies) - do what you've always done.
Layers - there are some keys to layering. 

• Base layer (the one closest to your skin) - should be a wicking material that will "suck" water away from your skin.  Cotton is your sworn enemy.
• Middle layers - decide how many of these you need.  The more wicking the better.  Also, the more zippers the better(they go up and down).  Climate control.
• Outer later - Should be wind proof.  It does not have to be super heavy or thick.  Zippers are still a good idea.

For anything above 40* I just wear a normal running shirt.
30*-40* I wear either two normal running shirts, or a heavier winter running shirt similar to a sweat shirt.
Below 30* I add the jacket.  As it gets colder I add more and more mid-layers.
I honestly don't wear arm warmers when it's this cold.  Those are more for the "I could be in a tank-top at the end of the race but a little chilly right now" temperatures.  

Legs
Regular running pants are not super thick, but obviously pants.
Winter running pants are expensive as hell but completely worth it.  They are thick and more wind proof than normal running pants.  They tend to fit better for running than normal sweat pants.
Running Tights  come in two flavors: fleece lined and not.  I recommend both flavors, not worn at the same time.
Underwear - should be a wicking material if you're wearing it.  Some pants and tights are meant to be commando. 
Long underwear - I tend to prefer tights to long johns but if you have strong preference in this direction, I recommend polypropylene long underwear.  Polypro is a wicking fabric, they also tend to fit the best for running, and have the unusual bonus of being pretty affordable.
For anything above 40* I either wear capris or maybe regular running pants.
30*-40* I tend to wear regular running pants too.  I am hot.
25*-30* - I tend to wear just winter running pants or fleece lined tights.
Below 25* - I start with combinations of not-lined tights and winter running pants and increase to fleece lined tights and winter running sweat pants as the mercury falls even farther.

Feet
Socks should be wicking, just like everything else.  Options include wicking sock liners or smart wool socks.  Doubling up on socks is an option, just try it on a short run first so you know how your shoes, socks and feet will cooperate with each other.
Shoes Those super light shoes that are all mesh on the uppers can work, but they are going to be cold.  Shoes are more dependent on the footing than the temperature.  In 5* and bare sidewalks, I wear my regular running shoes.  In 25* and snow and ice, I wear a shoe with better grip and more support. 
Yak Trax or similar These things are great in very specific conditions.  They are great on packed snow, freshly fallen snow, and all kinds of ice.  They are horribly painful on concrete/asphalt/etc.  So I only wear them when I know I'm going to have a snow pack to run on, or the snow is still falling and no one's sidewalks will be shoveled.

Hands
Gloves are a good idea.  Frost bite sucks people.
Those shirts with the thumb loops - also legit, and at some warmer "cold" temperatures, you may be able to get away with just those and no gloves.

Head and neck
Hats - seem to come in two varieties.  Fleece and wool beanie.  I wear both, wool beanie if it's a little warmer because I can feel the breeze come in and fleece if it's freezing too cold and I want no air of any kind touching my head.
Ear bands - some people prefer them to hats in the warmer cold temperatures.  Anyone who ran the 2012 Twin Cities Marathon has a new ear band they're probably dying to try out.  Between the hat and the ear bands, you'll know which you like.  Just go with it.
Neck/face gators - I rarely wear them, but every once in a while I'm glad I have them.  I have a fleece kind that is wind proof and I can lower it during the run as my face and neck warm up.

Other
Reflective Gear - it's basically night all the time here.  Wear your reflective gear!
Music - yes, I still run with my iPod, even when it's this cold.  No, I'm not worried about it freezing, although thanks for putting that image in my head.