Running when it's cold and/or rainy is completely different than running when it's warm out. If you happen to have access to a nice, cushy, cozy treadmill (jealous? me? noooo...) that's one option. But what if you want to run outside?
Layers, layers, layers
Layers are your friend. Regardless of the temperature, the first layer (both top and pants) should wick moisture away. Staying dry will keep you warm and prevent chafing as well. After that, wear one or more insulating layers, depending on how cold it is and how warm you want to be. You will probably want to be a little cold when you start running so you aren't burning up by the end.
If it's really cold, windy, or rainy, you should have a wind/water resistant jacket on top of everything. Prepare to spend some money on this, because it needs to breathe well. I have one similar to this from Brooks (about $75). It's nice because it's lightweight, has a hood, and is REALLY visible.
Don't forget your head and hands
You lose a lot of heat through your head, so when it's cold you'll want a hat. I usually wear a waterproof baseball cap, which works well for keeping sun and rain out of my face. When it gets cold, though, I use a fuzzy headband...it leaves the top of my head exposed, but covers my forehead, ears, and back of my neck.
Although you can pull your hands into your sleeves, I like convertible mittens. They keep my hands warm at the beginning, then as they warm up I can expose my fingers to cool them off.
Keep your feet warm
Many running shoes have a lot of mesh, and when it's cold my feet end up feeling like ice cubes, even if I'm wearing moisture wicking socks. Thanks to @elsewise's suggestion I put duct tape over the toe area on my shoe, which blocked enough wind that I could feel my toes through the entire run.
Prevent chapped lips
Blistex or Aquaphor are a must on your lips when it's really cold out - if you skip them, you may end up with really chapped lips. @ultrarunnergirl also suggested using Body Glide on your face to avoid windburn.
Running on snow/ice
If you are really feeling hard core, you can continue running on packed snow, slush, and ice. To maintain traction, I use Yaktrax - which are essentially chains for your shoes (click my shoe below to see them better). You stretch them over the soles of your shoes and wear them normally, and they work GREAT.
I wouldn't recommend using them on glassy ice, although they do help a little. But if there is ANY traction to be found under your shoe, Yaktrax will find them. I found that although they were noticeable, they were comfortable and I didn't have to adjust my stride too much. Plus, they work great when you're shoveling the walkway too!
Keep your shoes dry
This isn't really about comfort, but you should make sure your shoes dry out thoroughly if they get wet. After you take them off (you unlace them rather than just kicking them off, right?), pull the insert out. Put your shoes in a dry place, and don't lay the inserts flat or you may end up with mold. Some people also put crumpled up newspaper in the shoes, although I haven't tried that. The key is to prevent yuck from growing in them. Yes, that's a technical term.
What did I forget? What do you use when you run in crummy weather?
-Bill
