Is there any such thing as a famous world martial arts tournament?

Question

You know like the ones fighting games such as Tekken.

Answer 1

Every 2 years there is the submission tournament ADCC in Abu Dhabi.  The closest thing left since the Grand Prix in Pride is gone.

Answer 2

There is still one in Long Beach every year that is pretty big, but I've heard that attendance and interest has been waning with the new management.

Answer 3

Yes.

A few that I have heard of:

UFC

K1

Affliction

PRIDE

Early UFC was more "Tekken-like";

The matches were like "wrestler vs. ninja" and "kung-fu vs. thai-boxing"

The only people who won consistently were the people who practiced lots and lots of sparring and/or wrestling/grappling, so the competitions evolved into what we now call MMA.

In the early days, "MMA" described the rules of competition - any style vs. any style.  

Nowadays (about 15 years later?), "MMA" describes the fighting style that evolved as a result of MMA competitions - kickboxing, clinch fighting, and groundfighting mixed together.

Note:

Judo evolved the techniques that work best under the rules of Judo competition.

Thai boxing evolved the techniques that work best under the rules of Thai boxing competition.

BJJ evolved the techniques that work best under the rules of BJJ competition.

MMA evolved the techniques that work best under the new set of rules of MMA competition.