I normally don't use dragons all that often, but my previous campaign centered around a dragon that was pretending to be the returned king of a large region that had been prophesied. So the dragon had badgered/threatened some lesser dragons into helping him, but for the most part he was just the power behind the distant throne. He was also using his own mother (she was not a willing participant) to magically create half-dragons of various forms.
Funny thing is for various reasons they never actually fought the dragon (although they did fight a few others). They managed to find and free mommy dearest and
she chased off her imposter son.
As a general rule the older the dragon, the more tactical and less likely they are to ever get into a direct confrontation. Young or even some adult dragons are more likely to engage directly, but that tends to weed out the stupid or unwise ones. The ancient ones? They're far more likely to use others as cannon fodder and to have schemes that unfold over decades and centuries.
In battle, all but the youngest are never going to get into melee with PCs if they can at all avoid it. They'll use hit-and-run tactics using either breath weapon or bombarding from on high. They'll also do everything in their power to set up unfair fights; if absolutely necessary they'll flee to plot revenge and fight another day. It also depends on the type of dragon we're talking about of course. White dragons tend to be brutes, black dragons are schemers and so on.
In my current campaign the group is in the teens and have yet to face a single dragon. Not sure they ever will. On the other hand I do have a dragon war (led by mommy dearest and her now subservient son from the previous campaign) that's kind of rattling around. Maybe next campaign, with part of the campaign enlisting the help of the good dragons of the world.