I've had a few interesting dragon encounters over the years. As a player, by FAR the most memorable was in 2E when we finally worked our way through a nasty cavern system to get to the inner lair, the dragon was asleep! We prepared ourselves, and planned to let loose our highest level spells and magic items at it at once. We should have wondered what was up when the DM made us roll for initiative, but no one thought anything of it (in 2E, each round you declared your action, then rolled initiative, allowing actions to be interrupted). We unleashed Hell... on a poor tied up kobold that had the illusion of the dragon around it. All our best stuff went off at once, because you couldn't change the action once declared. Immediately, the real dragon got a surprise round on us, when he used his fire breath weapon on us from above! We did eventually defeat it, but only 2 out of 7 of us were still standing, with 3 of us completely dead (including me). This was so good, I stole the idea for a 5E game using a White Dragon and a polished ice wall mirror.
As a DM, one of the most interesting and fun dragon encounter never involved fighting the dragon at all. The party had to sneak into to lair of an ancient green dragon to retrieve lost elven artifacts. They knew they had no chance in a fight, since they were only level 3. They worked their way into the lair, and found the dragon asleep, facing away from them. The entire area was lit by a fungus, so light wasn't an issue, and they saw the survivors of the last adventurers to try this, tied and gagged on the far side of the cave with zombies guarding them. The artifacts they were looking for was adorning an elven corpse hung on a series of sticks like a puppet, right on top of the pile of coins that would surely make noise if disturbed. They could go for one or the other, but doing both would certainly risk waking the dragon... so of course they went for both. The rogue sneaked across the room to the prisoners (objecting heavily to being told NOT to go for the loot), while the sorcerer went for the artifacts. The sorcerer used levitate and pushed off from the wall to get the artifacts, making no noise and having no problems. The rogue found the "zombies" were humans set up like the other corpse was, then woke and untied the first prisoner... who immediately began to scream bloody murder!
Everyone freaked out, drew weapons and moved to fight the dragon... who never moved. The rogue freed and woke another prisoner, who was freaked out, denying the PC was real. The last prisoner was semi-lucid, and after being convinced the party was in fact real, explained that the ancient dragon who terrorized the forest has been dead for years. Her youngest son had taken over the horde, and used tricks to make everyone believe that his attacks were hers, since it would greatly deter thieves and would be dragon hunters. It had a cruel streak, like his mother, and used various illusions and the puppets to torment them until their minds cracked. They freed the prisoners, took the artifacts and only a small pouch of gems, then fled (they expected the young dragon to return, and didn't want to face it). They then raced through the forest maze around the lair while the young dragon threatened its minions to find the thieves, periodically flying overhead, but never finding them (I had a series of challenges based on how long they took in the lair, and if they took too long, the dragon would catch them). In the end, they escaped without ever facing a real dragon.