What happened to the Dragons???

Everybody remembers all the cool dragons Tokien wrote about: Smaug, Ancalagon the Black, Scatha the worm, and so forth. Everyone should also know that all the famous dragons genarally get killed.
But what happened to all the other dragons? Tolkien said that Melkor created a bunch and that the dragons reproduced, but what happened to them? Did they die or what???
The only thing Tolkien really says is:

It was rumored that Dragons continued for many centuries to inhabit the Norteren Waste beyond the Grey Mountains, but no tale speaks agian of these evil, yet magnificent, beings.

So what happened??