I love dragons. Shortly after I started playing AD&D, I read the Dragonlance books so the whole, "Dragons are awesome, epic and cool," thing stuck with me. Since my players tend to want generic fantasy, a.k.a. Forgotten Realms, dragons aren't as legendary as I have them in my homebrew setting, but I still make the effort to make them interesting, memorable and personalities that are larger than life.
A for instance would be a shadow dragon that the group encountered in a mirror-verse situation. A tower had been built up around a Moonwell, and Ordalf had used a Mythal to distort the magic of the Moonwell to divert to the Shadowfell instead of the Feywild (certain Moonwells are portals to the Feywild).
The tower was a trap that led people into it and through the portal where shadow demons, or simply exposure to the Shadowfell, killed the people on the other side. This fed the corruption of the Moonwell, which in turn fed the corruption of the Moonshaes. A coven of hags tricked people into going through the portal. On the other side is a mirrored version of the tower and the Moonshaes. One of the beings tricked into going through was a young red dragon by the name of Angevordin. His innate nature made him strong enough not to die but corrupted him into becoming a shadow dragon. And he has been trapped here ever since, growing in size and power and tormenting any beings that came through and collecting their treasure for himself.
Enter the PC's. I played him up as a bit cat-like, cunning, manipulative but very charming and even through his arrogance, having a sly sort of wit. The players loved him so much that they made a deal with him that if he didn't eat them and helped them get out, that they would come back with magic to free him (he was simply too large and didn't have the magic required to open the portal himself). So even after they got the McGuffin that helped them get out before dying to the Shadowfell's corruption, they came back of their own volition and freed him, knowing that he was inherently evil and would probably do evil things once freed.
He's essentially now a friend to the party. The kind of guy who you know is probably not a good person, but he's been good to you and you like him, so you hang out every so often, have some laughs, and part ways until next time.
So yeah, that's how I like to play dragons. Big personalities, a bit over the top, imposing, impressive, powerful and yet always interesting and a step removed from the every day. Something that leaves an impression. The players themselves might not remember the aboleth they fought, but if they ever encounter a dragon, they'll always remember it.