|Putin doing Judo (looks like striking...)|
Whether it is punching, kicking, elbow strikes, or eye gouges, there has to be some percussive techniques in martial art. In aikido, O-Sensei is often quoted as saying "70% of aikido is atemi."1 In aikido and jujutsu we use the strike as a distraction for the real technique, or as a quick pain to give a brief second of time to perform a lock or throw. Some arts have come to specialize in the percussive parts of the art, or practice the striking as a sport aspect. Tae Kwon Do goes to an extreme in this and specializes in the kicking aspect of striking, again for the sport aspect.
Tai Sabaki/Whole Body Movements
Whole body movement encompasses a couple of different ideas, all lumped under one heading. The general idea is body movement in relation to the opponent, often to get out of the way of an attack. It includes cutting angles, getting to the dead side, and moving your body of the line of attack. These are mainly represented in Jujutsu and Aikido by irimi and tenkan.
Nage Waza/Throwing Techniques
Joint locks are another necessary part of a martial art. Aikido and jujutsu often uses joint locks to lead to throws. Because strength is not a defining factor, this is one of the ways that smaller people can use martial arts on larger people. There are basically two categories of join locks, based on the joint that is being manipulated. Large joint locks, and small joint locks. Large joint are things like the shoulder or elbow. Small joints are things like wrists, fingers, or ankles. These are generally controlling techniques, however, with additional pressure, they can be used to break people as well. This covers a lot of grappling techniques, both ground grappling and standing grappling.
These maybe something specific to throwing arts, but as a personal opinion, something like this should be in every martial art. Ukemi is almost a whole art in itself. It is the art of safely receiving a technique. This will often be how to safely fall from a throw. I think this should be in the list because of all the things I've learned in martial arts, falling is the one I use the most often. Being able to fall and not injure yourself is an important life skill in general.
I know not all martial arts have a weapons program in their curricula, but I think this should be part of anyone's knowledge who wants to call themselves a martial artist. I've already written on why the study of weapons is an important. But suffice to say, it should be part of your studies, in my opinion.
1 Aikido Groundfighting: Grappling and Submission Techniques by Walther G. Von Krenner, Damon Apodaka, and Ken Jerimiah