Comets are different to asteroids in their origins. They can come from the Oort Cloud, a shell of icy bodies on the edge of our solar system; or the Kuiper belt, a band of icy objects beyond Neptune's orbit.
The first comet this year is Comet Pan-STARRS, which will pass Earth about 100 million miles away in early March. If it doesn't fall apart under the sun's gravity, it'll put on a good light show. The best time to view the comet will be at sunset March 12th and 13th, and we will have a crescent moon at that time.
In November and December, comet ISON will pass within 1 million miles of the sun. If that comet survives, we will get another brilliant light show before it passes Earth just after Christmas at a distance of around 40 million miles.