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According to the Draconomicon, dragons can live to up 1500+ years (although rarely one lives up to this long). Their lifespan is incredibly long, but they certainly are not immortal.

Dragons lives have 6 stages, which are:

Wyrmling: Newly hatched dragons. These are born already with a "general" grasp of the world and full array of abilities (although weaker than adult dragons). These stay with their parents for some few years, after that their parents abandon them for them to live their own lives.

Young: Young dragons, not yet adults are the most ferocious and territorial ones, often scorching entire mountains, marking it as their territory. These  have roughly the size of a horse or a little bigger. Dragons and their offspring often retain a relationship of affect, even resorting to them when in need of help, but never share territories. Some few treat their parents as rivals.

Adult: Fully grown, wiser dragons, already with a hoard (treasure) and a lair, these are not as aggressive as young ones, and prefer long term schemes, resorting not as violent means as the young ones do, such as building relations with merchants, cities & etc. Adult dragons often move their lairs or expand their territory dramatically. Due to this, adult dragons are the most likely to start conflicts with other wyrms.

Elder: Elder dragons are wise. Already have a fixed lair and a big hoard, these are ones of the most cunning ones, often brewing very long term plans and ingenious schemes. Those are very influent, having minions and wide relationships. He fully understands the capabilities of other humanoids and know how to use them. Very often they have a wide influence over the kingdom they live in. Many times even holding the king and the court as its puppets.

Ancient: When dragons reach this stage, they truly doesn't have anything more to do. Being basically one of the most powerful creatures to walk the earth, having hoards that are treated like legends, their names being known far and wide, most of them pass their time hibernating, counting their hoard, inspiring humans to go to war, attacking other dragons, studying... You can say this is the stage of a dragons like when he is "free" to do whatever he wants.

Twilight: On this stage of life, which normally comes within a couple of decades of its maximum lifespan, its the only period of their lives where they grow weaker rather than stronger. Most of the dragons don't wish to wither away and die, instead consuming his entire hoard and parting away in a final journey, burning the rest of its power in a mighty display of glory and fury. Some of them ravage entire civilizations, challenging the mightiest humanoid heroes to fight against them, searching for a glorious death or even invading other dragons, usually lifelong rivals, to end everything in a huge and spectacular conflict which can tore an entire nation apart.

Some very few resort to forbidden means to extend their lives, the Dracolichs, or undead dragons that use magic and forbidden rituals to keep on living, often living for so long that their entire bodies rot and decay, transforming into skeletal dragons.