In the Japanese version of X-Men Vs. Street Fighter, every character has unique pre-fight dialogue with Apocalypse. These short conversations were removed from the non-Japanese versions of the game, but thanks to shmuplations, you can read English translated versions of this dialogue below.

If you use cheats to use Apocalypse in the single player mode, he does have dialogue with himself -but he uses Magneto's lines.

Cammy

Cammy:

Target Apocalypse acquired...
Eliminate!

Apocalypse:

Welcome, Cammy, and farewell.
Your short, pathetic life ends here.

Behold, the true form of Apocalypse!
And now I shall take your life!

Chun-Li

Chun-Li:

Are you Apocalypse?
Don't move! You're under arrest!

Apocalypse:

Arrest? Me? Hahahaha!
Chun-Li, enough of this charade.

Behold, my true form!
And now I shall take your life!

Cyclops

Cyclops:

I've finally got you now, Apocalypse!
This is the end of your schemes!

Apocalypse:

Did you think you could capture me?
Cyclops, the defeat will be yours!

Behold, my true form!
And now I shall take your life!

Dhalsim

Dhalsim:

Apocalypse...
Your lost soul has still not attained enlightenment...

Apocalypse:

Dhalsim, you miserable fraud.
Have you come to capture me...?

Behold, the true form of Apocalypse!
And now I shall take your life!

Gambit

Gambit:

Game's over, mon chere.
You wanna get a prayer in?

Apocalypse:

Gambit, you insignificant petty thief.
You are the one will die here.

Behold, the true form of Apocalypse!
And now I shall take your life!

Gouki/Akuma

Gouki:

.............

Apocalypse:

Gouki! No matter how strong you become, you are still but a paltry human being.

Behold, the true form of Apocalypse!
And now I shall take your life!

Juggernaut

Juggernaut:

Uoaaaaarghhh!
Are you Apocalypse?!

Apocalypse:

Juggernaut, you gigantic fool.
It is time for you to learn that there are others stronger than you.

Behold, the true form of Apocalypse!
And now I shall take your life!

Ken

Ken:

Are you Apocalypse?
I've give you one minute before I KO you. There's others waiting after you!

Apocalypse:

Ken, you insolent human.
Are you saying you can defeat me?

Behold, my true form!
And now I shall take your life!

Magneto

Magneto:

Apocalypse, you have made a grievous mistake... you have angered me, Magneto, the Master of Magnetism.

Apocalypse:

Magneto, you are a laughable fool.
Have you come to capture me...?

Behold, my true form!
And now I shall take your life!

Nash/Charlie

Nash:

....
Well then, would you mind coming with me, Apocalypse?

Apocalypse:

Miserable Nash.
Do you presume to think you can capture me?

Behold, my true form!
And now I shall take your life!

Rogue

Rogue:

I knew you were behind this, Apocalypse!
Well come on then, sugah!

Apocalypse:

Rogue, you foolish mutant.
You and your friends never had any chance against me.

Behold, the true form of Apocalypse!
And now I shall take your life!

Ryu

Ryu:

So you're Apocalypse.
Time to fight! Let's see how you like the power of my fists!

Apocalypse:

Ryu, the wandering warrior.
Your fist, like all the others, will not stop me.

Behold, my true form!
And now I shall take your life!

Sabretooth

Sabretooth:

Heh, you don't look that tough!
Birdy, we're eating as soon as we get home!

Apocalypse:

Sabretooth, you foolish savage.
It is the two of you who have fallen into my trap.

Behold, the true form of Apocalypse!
And now I shall take your life!

Storm

Storm:

There's no escape, Apocalypse.
Release those you have taken!

Apocalypse:

Storm, Mistress of the Elements.
I'm sorry, but I cannot grant your wish.

Behold, my true form!
And now I shall take your life!

Vega/Bison

Vega:

You have the temerity to show up here, Apocalypse!
Your age has long since been over!

Apocalypse:

Vega, do you think really think such lowly garbage as yourself has any chance against me?

Behold, my true form!
And now I shall take your life!

Wolverine

Wolverine:

Apocalypse, I knew it was you!
Ok bub, today is the day you die!

Apocalypse:

Wolverine, you miserable berserker.
Do you think those claws of yours can stop me?

Behold, my true form!
And now I shall take your life!

Zangief

Zangief:

Huh? I dunno who you are...
You wanna see how you measure up to my Iron Body?

Apocalypse:

Zangief, you are a miserable fool beyond saving.
Do you think have the slightest chance against me?

Behold, the true form of Apocalypse!
And now I shall take your life!