Is there any indication given in the Alien movies or literature of how long an Xenomorph lives for? It occurred to me that given a limited number of potential hosts ( as per the colony on LV-426, the number of suitable gestation vessels would soon be depleted as would any other sources of food.
Ripley claims in "Aliens" that "one of those things managed to wipe out my entire crew in less than 24 hours".
I presume that the first Alien film shows us the entire cycle of egg hatching, implantation by facehugger, chestburster and xeno taking crew members (to cocoon them and transform them into eggs it seems), over a period of 2-3 days max. (One for the setting down on LV-426 and facehugging, and 8 hrs plus for Kane to be unconscious, and then the 24hr period while the alien hunted them out one by one on the Nostromo).
A maximum of 48-72 hours seems reasonable for these events to have taken place, even if there's no concrete information in the script or novelisation as to exactly how long the time period is from first contact to the expulsion of the alien from the Narcissus... and although we don't know for sure how long the alien would have remained alive if not killed, there is a mention on the DVD commentary about the idea that the alien was "sleeping" inside the shuttle because it was nearing the end of its natural life cycle and looking for a place to curl up and die.
The periods of gestation and hatching seem to get even shorter in more recent films (although my knowledge of books and comics is too limited to comment on those), but speaking of the first and second film, the xeno stage's life seems to be around 3 days or so if it was ready to die by the end of the first movie's events, and in "Aliens", the adult warriors appear to be in a hibernation state in their nest, semi-lodged into the walls.
If taking into account the idea of the lifespan of the xeno from egg to adult form, though, this could be hundreds, or even thousands of years to include the egg-stage dormancy. The adult form is evidently quite short-lived in comparison.
I was watching a video on Alien and they said that the Xenomorph wasn't hunting Ripley when it was in the escape pod, rather it was looking for a quiet place to die. They said the color change (light to dark) was showing it's lifespan, the older it got the darker it got. I have yet to fact check this but I found it on youtube. The name of it is 25 things you didn't know about Alien (read the exact claim in this page), also see the video, you can find the exact spot at 12 minutes and 31 seconds into the video. Youtube wasn't working so I had to use a different site.