There are four major styles of Karate today: Shito-ryu, Goju-ryu, Shotokan-ryu, and Wado-ryu. A brief description of each one is provided here.
Shotokan-ryu, which was founded by Funakoshi, came from Shorin-ryu (from Shuri-te), and utilizes long linear stances and physical power. This style was one of the first styles to be introduced to Japan in the 1920's. Powerful kata such as Bassai (Shuri-te) are typical of this style.
Goju-ryu was founded by Miyagi. It came from Shorei-ryu (from Naha-te and Tomari-te), which utilize up and down stances and internal breathing power (known as "hard and soft" techniques). Kata such as Sanchin (Naha-te) and Rohai (Tomari-te) demonstrate these techniques well.
Shito-ryu was founded by Mabuni. It is a combination of Shorin-ryu and Shorei-ryu, which makes this style a lot like a combination of Goju-ryu and Shotokan-ryu. Shito-ryu is fast, but is still powerful and artistic. Its kata include the same kata as Shotokan-ryu and Goju-ryu, as well as some artistic Chinese white crane kata such as Nipaipo. Shito-ryu also practices with Kobudo (weapon arts) and sometimes Iaido (sword arts) as part of the style, which makes Shito-ryu fairly unique among the modern Karate styles.
Wado-ryu is a derivative of Shotokan-ryu. It was founded by Ohtsuka, a student of Funakoshi.