Krav Maga-Israeli martial arts. used by the israeli military.
Muay Thai- Brutal enough to be called a martial art even though some see it as a combat sport. focuses on using the hardest joints of the body (ie. knees and elbows) as well as kicking using the shin.
Jeet Kune Do-Brcue Lee's creation.
Karate (varied)- system of unarmed combat (originally developed in okinawa, japan, although other forms of karate exist today). Popular with the west (im not really sure why though).
Wing Chun- hard chinese martial art. pretty popular. sometimes called "chinese street fighting." effective, as well as dirty.
Ninjutsu- Literally, this martial art has no limitations and is just downright dirty and unsportsmanlike. That said, it is also one of the most effective and deadly martial arts in the world (when studied properly of course). Not so sure about the popularity of it though... but i can assure you, it is extremely effective.
uhh. yea, there's probably more, but i dont wanna tire out my fingers
remember, martial arts differ from combat sports... martial arts have no limitations, whereas martial sports are used in competitions and sparring and do have limitations on what can be used, so as to not sustain permanent injuries/disabilities/death or any unwanted physical condition brought on by fighting. However, many martial arts can also be applied to a sport context given the omission of death blows, groin shots, or any "unsportsmanlike" techniques or abilities.
so, that's why i didn't add boxing or wrestling...