--Physical Immortality--
Unless destroyed, the physical body existing forever, sustaining the mind for those who do not believe in the existence of thought beyond physical life.

--Spiritual Immortality--
The existence of a mind/spirit/soul outside of physical existence, surviving the death of the physical body.

--Gene Immortality--
The concept of immortality through one's children carrying on some semblance of your being in their genetic makeup.

--Remembrance Immortality--
Being 'immortlized' by your great deeds, society/family's memory of you and your accomplishments and ideals.

Sourced

• A toy which people cry for,
  And on their knees apply for,
  Dispute, contend and lie for,
  And if allowed
  Would be right proud
  Eternally to die for.
  • Ambrose Bierce, The Devil's Dictionary.

Dictionary of Burning Words of Brilliant Writers (1895)

Reported in Josiah Hotchkiss Gilbert, Dictionary of Burning Words of Brilliant Writers (1895).

• Immortality! We bow before the very term. Immortality! Before it reason staggers, calculation reclines her tired head, and imagination folds her weary pinions. Immortality! It throws open the portals of the vast forever; it puts the crown of deathless destiny upon every human brow; it cries to every uncrowned king of men, "Live forever, crowned for the empire of a deathless destiny!"
  • George Douglas, p. 337.

• The soul secured in her existence, smiles
  At the drawn dagger, and defies its point.
  The stars shall fade away, the sun himself
  Grow dim with age, and nature sink in years,
  But thou shalt flourish in immortal youth,
  Unhurt amidst the war of elements,
  The wreck of matter, and the crash of worlds.
  • Joseph Addison, p. 337.

• Earthly providence is a travesty of justice on any other theory than that it is a preliminary stage, which is to be followed by rectifications. Either there must be a future, or consummate injustice sits upon the throne of the universe. This is the verdict of humanity in all the ages.
  • Randolph Sinks Foster, p. 337.

• Without a belief in personal immortality, religion surely is like an arch resting on one pillar, like a bridge ending in an abyss.
  • Max Muller, p. 337.

• Whence comes the powerful impression that is made upon us by the tomb? Are a few grains of dust deserving of our veneration? Certainly not; we respect the ashes of our ancestors for this reason only — because a secret voice whispers to us that all is not extinguished in them. It is this that confers a sacred character on the funeral ceremony among all the nations of the globe; all are alike persuaded that the sleep, even of the tomb, is not everlasting, and that death is but a glorious transfiguration.
  • François-René de Chateaubriand, p. 338.

• See truth, love, and mercy in triumph descending,
  And nature all glowing in Eden's first bloom!
  On the cold cheek of death smiles and roses are blending,
  And beauty immortal awakes from the tomb.
  • James Beattie, p. 338.

• Tell me why the caged bird nutters against its prison bars, and I will tell you why the soul sickens of earthliness. The bird has wings, and wings were made to cleave the air, and soar in freedom in the sun. The soul is immortal — it cannot feed upon husks.
  • Randolph Sinks Foster, p. 338.

• I feel that I was made to complete things. To accomplish only a mass of beginnings and attempts would be to make a total failure of life. Perfection is the heritage with which my Creator has endowed me, and since this short life does not give completeness, I must have immortal life in which to find it.
  • Randolph Sinks Foster, p. 338.

• It is our souls which are the everlastingness of God's purpose in this earth.
  • William Mountford, p. 339.

• May we be satisfied with nothing that shall not have in it something of immortality.
  • Henry Ward Beecher, p. 339.

• Heaven begun is the living proof that makes the heaven to come credible. Christ in you is "the hope of glory." It is the eagle eye of faith which penetrates the grave, and sees far into the tranquil things of death. He alone can believe in immortality who feels the resurrection in him already.
  • Frederick William Robertson, p. 339.

• The nearer I approach the end, the plainer I hear around me the immortal symphonies of the worlds which invite me. It is marvelous, yet simple.
  • Victor Hugo, p. 339.

• No martyr ever went the way of duty, and felt the shadow of death upon it. The shadow of death is darkest in the valley, which men walk in easily, and is never felt at all on a steep place, like Calvary. Truth is everlasting, and so is every lover of it; and so he feels himself almost always.
  • William Mountford, p. 339.

• Let a disciple live as Christ lived, and he will easily believe in living again as Christ does.
  • William Mountford, p. 339.

Unsourced

• Immortality is not a dream,...but a goal in the lives of those who want it.
  • M.El Banna

• Being born is not a crime, so why must it carry a sentence of death?
  • Robert Ettinger

• Since thou hast no benefactor in this world, thy having one in the next world will be all the more pleasant.
  • Anonymous

• I don't want to achieve immortality through my work; I want to achieve immortality through not dying. I don't want to live on in the hearts of my countrymen; I want to live on in my apartment.
  • Woody Allen

• I shall always believe in immortality ... as long as I live!
  • Leonid S. Sukhorukov, All About Everything (2005)

• Millions long for immortality who do not know what to do with themselves on a rainy Sunday afternoon.
  • Susan Ertz

• The only thing wrong with immortality is that it tends to go on forever.
  • Herb Caen

• A man looking onward to an immortal life, on whatever grounds, exhibits to us the human soul in an enobled attitude.
  • William Whewell

• I do not believe in the immortality of the individual, and I consider ethics to be an exclusively human concern without any superhuman authority behind it.
  • Albert Einstein

• We do not believe in immortality because we can prove it, but we try to prove it because we cannot help believing it.
  • Harriet Martineau

• We want to live forever, and we're getting there.
  • Bill Clinton http://www.rand.org/scitech/stpi/ourfuture/Rosetta/millennium.html

• Immortality: a fate worse than death.
  • Edgar A. Shoaff

• Give me immortality or death.
  • Nick de Jongh

• Clov: Do you believe in the life to come? Hamm: Mine was always that.
  • Samuel Beckett, Endgame (1958)

• That which is the foundation of all our hopes and of all our fears; all our hopes and fears which are of any consideration: I mean a Future Life.
  • Joseph Butler, The Analogy of Religion (1736)

• If you were to destroy in mankind the belief in immortality, not only love but every living force maintaining the life of the world would at once dry up. Moreover, nothing then would be immoral, everything would be lawful, even cannibalism.
  • Fyodor Dostoevsky, The Brothers Karamazov (1879-1880)

• Other world! There is no other world! Here or nowhere is the whole fact.
  • Ralph Waldo Emerson, Natural Religion

• No young man believes he shall ever die.
  • William Hazlitt, On the Feeling of Immortality in Youth (1827)

• He had decided to live forever or die in the attempt.
  • Joseph Heller, Catch-22 (1961)

• The first requisite for immortality is death.
  • Stanislaw Jerzy Lec

• We are made to be immortal, and yet we die. It's horrible, it can't be taken seriously.
  • Eugène Ionesco

• Immortality is the only thing which doesn't tolerate being postponed.
  • Karl Kraus, Sayings and Contradictions (1909)

• Strive not, my soul, for an immortal life, but make the most of what is possible.
  • Pindar, Pythian Odes

• Let us be persuaded ... to consider that the soul is immortal and capable of enduring all evil and good, and so we shall always hold to the upward way and pursue justice with wisdom.
  • Plato, Republic

• We feel and know by experience that we are eternal.
  • Baruch Spinoza, Ethics (1677)

• Our current obsession with creativity is the result of our continued striving for immortality in an era when most people no longer believe in an afterlife.
  • Arianna Huffington, The Female Woman (1973)

• When asked about his opinion on the hereafter. “One world at a time.”
  • Henry David Thoreau

• When all desires that dwell within the human heart are cast away, then a mortal becomes immortal and here he attaineth to Brahman.
  • Upanishads, Katha Upanishad

• Spring—an experience in immortality.
  • Henry David Thoreau

• Immortality goes on for too long to be taken seriously, and so doesn't last long enough to be fully appreciated.
  • Anonymous

• Posterity is just around the corner.
  • George S. Kaufman

• Infinity converts that which is possible into the inevitable.
  • Norman Cousins