Disclaimer: Right, after looking at the life cycle node above, I decided it wasn't enough as there is a lot more information that can be gathered from the Alien saga. So, all of this information is based on things seen in the films. The books, video games etc. are not part of this. Deleted Scenes do not count. The newborn does not count either, as there isn't anything to really say about it or anything to gather from the film. This life-cycle wil be mainly based on the human host variant we see in Alien, Aliens and Alien: Resurrection.
1. Egg
The egg is layed by a fertile Queen. Large numbers of eggs are usually created in short amounts of time, and are usually placed near each other in a hive. Eggs are the dormant home of the face hugger, and they have the ability to keep the face hugger alive for long periods of time. The egg seems to have some sort of motion sensor capability, so when potential hosts move near to the egg, it knows it is time to hatch. This ability may take some time though, for example when Kane fromt the first Alien movie examines one of the eggs, it doesn't open instantly. Neither do any of the other eggs, which may give way to some sort of intelligence and a form of communication within the eggs. How they communicate is unknown, though it is safe to assume it is some sort of telepathy. It could be sound, but would have to be so high that people would not be able to hear it.
Once the host approaches and the egg hatches, the face hugger is revitalised from its hibernation and thus attempts to latch onto the host. The egg presumably "dies" after this point (if it can be considered alive in the first place).
2. Face Hugger
The face hugger is so called because it latches onto the host's face in order to plant the alien embryo inside it. It's body is perfectly designed for this task, with long finger like limbs in which to grasp the host, and a large tail about 2-3 times the size of its body used to jump long distances. When it latches on, the host falls unconcious, how it is unknown. We do know that the face hugger then controls the oxygen fed into the host (or whatever the host breathes), so it may lower the oxygen count to a point where conciousness cannot be achieved. After latching onto the face, the tail wraps around whatever it can (in a human's case, the neck) and is impossible to remove without ripping the host's face off with it. The face hugger's blood is concentrated acid, so any attempts at cutting it off would be extremely dangerous to the host and anyone nearby.
During this time, the embryo is placed in the victim's chest, where is starts to gestate. After completing its job, the face hugger falls off the host and soon dies. Evidence that it doesn't die right after falling off is in Alien, when they find the face hugger dangling under the lights, not next to Kane.
There seems to be another form of the face hugger, one that lays a Queen embryo. They seem to be identical to the original, but don't seem to die off afterwards. This may be so it can lay other embryos to protect the Queen. This is shown in Alien 3, when one egg is shown, yet two aliens are planted (inside Ripley and the poor dog). It seems to die after this.
3. Chestburster
At first, the 'burster seems to lodge itself into the vicitm's chest cavity, possibly below or between the lungs. How it gets here from the windpipe is unknown (just one of those plot holes, really). It is here where it starts its rapid growth process into a fully-grown chestburster. While inside, it probably affects the metabolism within the host, convincing it to eat more so the alien may grow quicker (shown in Alien, when Kane grew hungry quickly). The exact difference this makes is again unknown, but we can guess that it at least helps. During this gestation period, the embryo takes genetic information from the host and blends it with its own DNA. This may be so the new alien can adapt to its new surroundings quickly, and have a chance to survive the same way the host would in an enviroment (shown in Alien 3).
After a few hours, the host wakes up and assumes nothing happened, despite feeling bad (either due to the increased metabolism rate, or the large piece of unknown tissue lodged inside their chest cavity). A few minutes later, poissbly 20 to 40 minutes, the chestburster decides to force its way out of the ribcage and through the lungs, the muscle and skin. It quickly runs for cover, and dissapears. The host goes through a relatively short, but extremely painful death.
The Queen embryo has a much longer gestation period than that of a normal warrior. It seems to be around 1 week, judging from Alien 3. The host also seems to be concious for a much longer state, a few days worth maybe. The increased time of gestation is down to the fact that the Queen is larger, stronger and therefore a more complex being than the normal warrior..
4. Adult/Warrior
This is the final stage of development for the more common variant, the warrior. This form has already shedded at least one layer of skin and grown from 1 foot to about 7 or 8 foot in length (12 to 15 including the tail) Its form has noticeably changed from that of a snake-like creature to that of an unstoppable killing machine. This form is very ferocious, with great agility and strength. It can curl up into small crevices and walk up and down walls and ceilings. It has razor sharp claws on its hands and feet, as well as large teeth. The human variant (i.e. came from a human host) stands on two hind legs with two front arms, much like a human. It's tongue is an extra set of jaws, used as a great offensive weapon. The tail is used to keep it upright as well as another weapon.
The job of this alien is to protect the Queen at all costs, as well as gather potential hosts and take them back to the hive. It also has the job of creating the hive, assumed from Aliens. The walls of the hive are created so the creatures can blend into their surroundings easily, taking intruders by surprise ("They're coming out of the god-damn walls"! - Private Hudson). They may create this hive from the secretion that drool from their mouths, as both the walls of the hive and this are both very similar (i.e. dark and shiny).
They also seem to have the ability the eggs had, and that is telepathic communication. This is probably only used in conjunction with the Queen, as Warriors tend to screech at each other (as in Alien: Resurrection). They don't have eyes, and seem to navigate via sound as is suggested in Alien: Resurrection. They might be using some sort of radar much like the eggs, so they know where everything is (unlike Alien 3, where it showed the Alien's viewpoint in the chase scene near the end). This telepathy seems to affect chestbursters as well, as in Alien 3 the warrior knew of the growing Queen inside Ripley so it didn't attack her.
As this is the final stage, it is unknown if the Alien dies out after a while. If it does, it would not be of hunger as none of the hosts are eaten. The exception can be of the dog variant in Alien 3, where you see it eating one of the prisoners. This could be due to the Dog's DNA spliced with it's own (or the writers screwing up). The Alien can, however, survive in a vaccum (as in Alien at the end) so it is assumed that it doesn't breathe (Big bugger up! In Alien: Ressurection, one of the Aliens breathes on a plate of glass. Strike two for the writers!).
5. Queen
The Queen is the controller of the hive and communicates with all the Warriors that stemmed from her face huggers. The Queen stands at least 15 feet tall (possibly 30 or 35 feet including the tail), and has what seems to be 4 or 6 front arms with two hind legs {the human variant). When the hive is constructed, it is assumed that the Queen is placed right in the middle of it laying the eggs. While she is laying, the Queen is surrounded by a large ornate skeleton, mostly around the head, and is connected to a large bulbous egg sac. The queen either moves for space to lay eggs, the warriors move the eggs, or the sac extends to a new spot. It is safe to assume that the egg sac is connected to the Queen naturally and therefore gorwn, but it can be pulled off much like a lizard's tail. This seems to be a very painful experience though, so the Queen would normally stay put.
She also seems to possess a much larger intelligence than the other aliens. When Ripley burns an egg with her flamethrower, the Queen resonds by sending warriors in after her. When Ripley points her gun at the rest of the eggs, the Queen sees this as a threat and sends the warriors away in fear of her precious eggs being destroyed. She also knew how to work the elevator so she could go after Ripley. The Queen seems to actually care about the rest of the hive as well, something the warriors never show. When Ripley destroys all of the eggs, the Queen screams and chases after her in blind fury, disposing of her egg sac during this.
After the Queen, there are no more stages in the Xenomorph life cycle. Unless someone decides to introduce something new in Alien 5: The Resurrection is back (and this time, it's war!).
Sources:
http://www.alien-world.co.uk
Alien
Aliens
Alien 3
Alien: Resurrection