Some comets that appeared in 2013 are Comet Pan-STARRS and Comet ION. These two comets were visible in the Northern Hemisphere, and both were very bright in the night sky. Comet ION was the brighter of the two comets, but both were visible with the naked eye.
Comet Pan-STARRS appeared in the Northern Hemisphere as early as March 7th, with some of the best viewing nights around March 10th. Earlier in 2013, this comet was visible in the Southern Hemisphere.
In November 2013, Comet ION made an appearance. This comet was considered one of the brightest comets visible from the Northern Hemisphere for many years.