There are plenty of Western martial arts. Savate, boxing, Pankration, Capoeira, fencing to name a few. There is also Historical European Martial Arts (HEMA) which are attempts to recreate medieval martial arts from manuscripts written by the masters of the time.

It's worth a mention that 'martial arts' are generally only called that in the mainstream as a way of going 'Asian martial arts'. There are a great variety of western martial arts, but so many of them are either well-developed enough to have their own followings, or just seem second nature to those in the west, whereas Asian martial arts, with their 'flash' and odd names, have much more of a mystique.

But some things you might not consider, but are considered to be martial arts would be wrestling (The grapple variety, as opposed to the WWE variety), fencing, and boxing. There are -many- others, as well, though not quite as mainstream as those three.

hi! you may be interested in responses in these threads..

Europe

• Why are hand-to-hand martial arts so much more prevalent in Asia than in other areas of the world?

• I have a likely ignorant question about "fighting disciplines" and geography

• I often hear of how the Greek Spartans were History's greatest fighters. What was it about the Spartans that made them so fearsome? Did they put more emphasis on training physicality than most forces of the time, was their weaponry superior, did they employ ancient 'martial arts'?

• Did peasant classes in europe and the middle east develop their own self-defense martial arts?

• How applicable are those "Western Martial Arts" really?

• Western unarmed combat in the middle ages.

• In the High Middle Ages, what sort of unarmed combat training did knights receive?

• Hand to hand dueling

• plus several posts on jousting

Elsewhere

• Why is it that African Culture apparently never developed a martial art on par with Asian style martial arts like kung fu or jiujitsu? Or did they and it's just not well known?

• What were characteristics of the Native American/First Nations fighting methods, and how did they develop?

• Did India develop any martial arts traditions like their Asian counterparts? If so, how are the styles distinct and what weapons were used?