I like the Imperium (despite backing Chaos in Eternal Crusade) because despite all of their problems, the Imperium trods on, unbowed and unbroken, following the will (if not the spirit) of the God-Emperor of Mankind.

From falling from grace to becoming the oppressive society they are -- From almost-born utopia to war-torn hellscape -- over millenia of slow technological decay, religious zealotry and everything else, Mankind as a whole hasn't yet fallen to anyone. It's rooting for the home team, y'know?

Then I look at the space marines. Some are outright horrible towards people, while others happen to be the very essence of what they were made to be when they weren't conquering the stars -- Guardians of humanity. They gave up their humanity to become something more, to protect those now weaker than they themselves were.

The Imperium is just one, giant, tragedy that's unrolled over 10,000+ years that I just can't get enough of. Just imagine the scale of everything that's happened to them. Now realize that they have no damn intention of giving up, despite it all. IF that isn't worth admiration, what is?

Wait... what? There are something like hundred billions of human beings breathing at the same time in the galaxy at the 41st millennium, that's not what I call "on the brink of extinction" (i.e. don't steal our fluff you foolish mon-keigh!).

They are the same thing?

So, I heard you like tragedy *claps his hands, causing a harlequin troop to appear in the room in bright flashy lights*

*clear his throat* The story begins at a time when your ancestors were crawling at the depths of the oceans...

If the Emperor died and warp travel became impossible, those billions of humans would be seperated from eachother, unable to aid another world which is being ravaged by orks or tyranids. All would be left in darkness again. Humanity is on a knife edge.

No pity for the eldar, they are likely the cause of the warp storms of old night and the loss of the greatest age of human advancement. As for humans being close to extinction that's not far off, as mentioned without the astronomican the empire is dead. If about a quarter of the orks unite for a waagh then the humans are boned same with the necrons uniting. They are also in a loosing war with both the tau and tyranids. Also eventually Abaddon will get a crusade to go his way or be replaced by a competent leader. Of the major factions the eldar are the only group small enough to not pose an extreme threat to the empire.

I believe it's safe to say that eldar's ancestors crawled out of the ocean bed at some point of their species' development

I'm originally a Tau player (and still is), but as time passed, I grew to feel strong connection with Grey Knights and later got myself familiar with the Black Templars too. These are 3 pillars of my Warhammer fanboyism =)
I cant say which faction I like the most, they are different, special and interesting.
If I were to embody some person within the universe, I think I'd go with Black Templars

If I were to describe why I love this or that faction, this would reuslt into a lengthy post. So I'll try keep it short:

Black Templars live attuned with the true spirit of Warhammer, Imperium of Man and Emperor Himself. Crusading Humankind, ever steadfast, ever growing and expanding, ever relentless and pushing boundaries of impossible.

Grey Knights are grim guardians and warriors against the terrors that lurk in the shadows of mind and soul, against the perils that await in the Warp. They stand guard of the very Soul of the Humankind, being the very seed of the Emperor they continue His work. Very gothic, very noir daemonhunting organization, very secretive, their existence being unknown to the 99% of the people of Imperium.

Tau, young ambitious race with comparatively scarce population (apart other races) potentially naturally weaker but unexpectedly fast-developing, strong and cunning. Tau Empire is in many ways what Imperium of Man should have become: united under one purpose and idea of scientific progress and wonders of exploration. Opposed to the darkness of religious terror which Emperor strived to circumvent and root out for he knew that humans are prone to fanaticism.
Besides, tau are the only people that are just fragile (but stubborn to die) creatures against the harsh world, just like simple people of the Imperium and Imperial Guard.

My personal feelings apart, I really like all of the Warhammer races/factions this or that way and have certain particular interest in each and every one of them.

Well in that case the whole galaxy (except the orks) is "on the brink of extinction" because of the tyranids, necrons and Chaos threats, and it is mostly because everyone fights for survival that all the remaining races are still alive: from this point of view the Imperium (roughly said humanity) is just a bigger faction which does the same struggle for life than any other one - at least it still has many representatives.

Also, speaking of humanity, I find gue'vesa tsoldiers more worth of admiration than most of the imperial troups, since they freely fight for an ideal that encompass not only one single race.

The tragedy of their race is not about the death of those fools that sunk into hedonism, but the one of the eldar who forsaw the cataclysm and yet couldn't escape it in time. One must know that the craftworlders and the exodites aren't responsible at all for She Who Thirsts' birth - on the contrary they tried to prevent it through self-discipline and privation - to truly understand the tragedy of this race. After all, can you really judge a race for the misdeeds of a few individuals?

True, yet fortunately for them the Old Ones had great plans for their species and thus have enhanced them physically and psychically for the task

'Few' isn't really a good word.