Wasn't it implied in the Japanese version... *Ending spoilers*

[Dr. Casey]

... that Shadow planned to commit suicide?

[Zeromus_X]

It's pretty heavily implied in the English version too.

[Roto13]

I don't know if it can be any more heavily implied without him going "I'm going to kill myself, you know." :P

[Yar]

Superliminal messages? :p

[Zechs]

He opted out, and that is exactly what he did. Can't get more direct than that.

[blackmage_nuke]

I wasnt sure so i purposely got him to attack himself until he lost all his hp in the final battle to satisfy myself and have the question definitely answered.

[Unstoppable Pig]

I don´t think he actually killed him by stabbing himself, he just died when Kefkas Tower collapsed. Wasn´t there also at one point implied that Celes tries to kill herself instead just wanting to swim.

[KoShiatar]

Yes, Celes did try to commit suicide by jumping off a cliff. It is strongly implied in the Japanese version and in the English one as well that Shadow is going to stay in kefka's tower and not escape with the others, almost certainlt dying when the tower collapses.
He even tells Interceptor to go away without him.

[Exdeath]

What isn't shown is him putting a gun in his mouth, thinking twice about life, and deciding to live after wasting his one shot. The tower collapses before he escapes.

[scrumpleberry]

Erm, yup. He dead.

[Flying Mullet]

Shadow: Go on, Interceptor! Get going!
Shadow: Take care of yourself, boy...
Shadow: Baram... It looks like I can finally stop running... Come and find me
all right?

Sounds like he's ready to die to me.