Yes, there are numerous techniques that can kill without using weapons other than one's own body parts. They usually involve strikes against vital points, particularly around the throat or the neck, choking techniques or some combination thereof (particularly chokes that crush the larynx at the same time).
Are they necessary? That depends on what one does for living, where one lives and a myriad of other factors. For a vast majority of self-defense minded civilian folks, I don't think they are necessary.
However, I think that what one should look for are not techniques that can kill, but ones that will most effectively STOP the aggressor. Why crush the larynx, when you can compress the carotid artery and render the attacker unconscious? There are psychological, legal and other considerations that make "stopping" more important than necessarily "killing."
Obviously having weapons (guns or knives) make things "more equal." Yet, despite one's best efforts, one cannot be armed always. Some time ago, I read an interesting case presented in the "American Guardian." A pistol-armed home owner confronted a burglar at night, but a struggle ensued before he can get off a shot. The pistol was dropped. The burglar got on top of the home owner (mounted him) and started to choke the home owner. The latter was able to muster some strength and choke the burglar back, push him off and retrieve his gun.
Now, that particular home owner was lucky. He was apparently stronger and bigger than the burglar and was able to overpower the thug. Unfortunately, that may not always be the case for most folks.
There are those who claim that they will always be with a weapon (knife, gun, key chain, yada, yada). Certainly one should always endeavor to use a weapons or an improvised weapon in a self-defense situation. But a human being is not a machine and cannot always be on guard and may be disarmed before he can react. For that reason alone, I think that a complete "self-defense" system ought to include unarmed self-defense techniques.
Skorzeny