It would eventually land on Earth and establish the democrat party, continuing it's evil against mankind.

You can see what happened to it at the end of this…
"Please vote to preserve the unique character of Warren…" - Robert Duvall

True.
Here are the ways it would eventually die if it lasted so long.
Starve to death.
Get hit and killed by a passing meteor, asteroid, ship or anything else flying around out there.
Gets burned or melted if it comes close enough to a star.
If it survives long enough and gets pulled in by a planet's gravity then it would burn up as it falls through the atmosphere.
It it somehow survives that then the fall would kill it when it hits the surface.
"Please vote to preserve the unique character of Warren…" - Robert Duvall

I think while it may be able to survive the vacuum of space, eventually, it would probably just die. They are tough but certainly not immortal.
So many stories, so little time.

"If it fell back to orbit thought, it's ****ed."
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LOL, Definitely!

They are pretty durable. They can survive extreme cold and heat. If it floated in space, I think it could survive a while. It might be in luck if a ship came along.
If it fell back to orbit thought, it's ****ed.

I'm fairly sure that in the novelisation Ripley watches the charred tumbling creature eventually explode, due to the pressure difference.
It could be a different book I read though
Star
Stuff

"The Queen would've eventually re-entered LV-426's atmosphere, burned to a crisp, and splattered across the landscape."
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Agreed!

The Queen would've eventually re-entered LV-426's atmosphere, burned to a crisp, and splattered across the landscape.
The Alien alien was most likely killed by the shuttle's engine. Even if it wasn't, then it's drifting in interstellar space. If it ever comes into contact with another ship, it'll be when it is splattered like a bug on a windshield.
Thit and thpin!

Alien borrows heavily from A. E. van Vogt's short story Discord in Scarlet.
In that story, Xtl (or Ixtl if you prefer the name given to the creature in The Voyage of the Space Beagle) can survive in space indefinitely.
If we assume the Alien borrows other aspects of its life besides its method of reproduction from Xtl/Ixtl, then, yes, the Alien will float alive in space forever.
Requiescat in pace, Krystle Papile. I'll always miss you. Justice was finally served.

It would probably need to eat at some stage, or whither away

Eventually it's going to fall into the gravity well of a star or hit something. The Queen in Aliens was blasted out of the airlock and was last seen falling down. If the blast was strong enough it might have fallen back into LV-426.
While you're studying the ACTUAL effects of a vacuum on the human body.
Try throwing a few Orbital mechanics 101 lessons in there as well.
ROFLMAO.
this'll get you started
http://www.imdb.com/board/10090605/board/nest/261339853?d=264776121#264776121
I joined the Navy to see the world, only to discover the world is 2/3 water!

Remember that the Queen survived the flight to the Sulaco in the unpressurised landing gear well of the dropship, so they can go without oxygen and survive near vacuum for a period of time. Probably quite a significant one!

I think dormant is infinitely more reasonably than alive in the vacuum of space for an extended period of time even with acid blood which may contribute to the Xeno's rapid growth. Not that I put much, if any, stock in the AvPs (they are however just fine for comics and video games IMO) the queen was frozen (dormant) for 1K years and who knows for how many 1K year periods in AvP1.

Eventually it's going to fall into the gravity well of a star or hit something. The Queen in Aliens was blasted out of the airlock and was last seen falling down. If the blast was strong enough it might have fallen back into LV-426. Even if it survived the heat of re-entry it would certainly have been killed when it hit the surface.

I think it can survive in space for a long, long time (so I think the queen in Aliens is still alive in some dormant state or whatever), but it would not make any dramatic sense if it survived the engine blast triggered by Ripley.
The beast is done for.
They are not intended to be indestructible, by any version of the script (that I know of anyways).
I was looking back to see if you were looking back at me to see me looking back at you

Total Recall showed what would happen to a human in those circumstances, the water in your body and your blood begins boiling almost instantly.
Thanks for the laugh.
Now You wanna start learning your science from actual science?
I joined the Navy to see the world, only to discover the world is 2/3 water!

The problem with trying to survive in a vacuum is that the fluids in your body will start to boil, Total Recall showed what would happen to a human in those circumstances, the water in your body and your blood begins boiling almost instantly. The Xenos haven't evolved naturally, if you want a perfect killing machine you can design its biology to enable it to survive in a vacuum for a significant period. There are fluids called ionic liquids which theoretically can survive a vacuum for thousands of years before fully evaporating. It's possible that a sufficiently advanced technology could have created a liquid with similar properties that could also serve as the Xeno's blood.

You could add the queen at the bottom of the Antartic ocean if you really want to.
We have seen Xenos die in various ways and seen eggs hibernate for apparently long periods of time so who knows for sure what dead space or the bottom of the ocean would do to them.

Considering the nature of the beast it wouldn't surprise me at all if it managed to survive not only the engine exhaust blast but also the vacuum of space for an extended time. One thing we've learned about them throughout the movies is that they are very resilient.

It was wounded by Ripley's spear gun and then fried by one of the shuttle's engines so if it was still alive, it would be "one tough little son of a bitch".