The first 2nd Edition D&D game I ran and the d6 Star Wars game I ran back in the day are probably my strongest qualifications.
In the 2nd Edition Game, I selected monsters half-the-time literally by flipping the book open to a page and throwing whatever was there against the party. Made for some interesting combats since no-one (not even me) knew what was living in that cave they decided to explore.
The guy who always played wizards in my game went through 13 of them(he got so he could make them in 5 minutes or so). One of his wizards died and was resurrected by an artifact 8 times before he threw it into the ocean so it couldn't bring him back again when he died next - does it qualify you as a RBDM if a player has ditched an artifact so it won't bring them back to life?
The party also liked to hunt dragons, even though no fewer than 2 PCs died every time they hunted one. Like when they went after a Red Dragon and the guy with the custom Thief/Wizard class he'd designed (that he was very proud of) cast invisibility, silence, and spider climb and went ahead to scout out the dragon's cave.
I didn't even tell the player what happened, just rolled damage and described to the rest of the party the massive detonation of flame and body parts, melted tools, and smoldering spellbook-pages flying out of the cave. They didn't even blink, just shouted "it used it's breath weapon!" in unison and charged in... only to find the Red Dragon just waking up after being alerted by the flame trap the scout had set off. Two more PCs died in the first round.
In my d6 Star Wars game, we played off-and-on for 3 years and at the end of that, the group was still scrambling for work, always just barely on the edge of being broke since anytime they got a huge payout, their ship cost so much to repair that they spent it all fixing it up - or they'd get screwed by their irreputable employers and then blow more time, credits, and ammo getting revenge.
The ship had real character too, originally a stock YT-1300, by the end it was simultaneously bad-ass and beat-to-hell from all the parts that had been blown off and replaced with replacement parts of various quality (from a Turbolaser stolen off an Imperial Corvette to a hull-patch made of plywood, scrap metal, and emergency hull-sealant), and all debris fields, anomalies, corrosive atmospheres, and fire-fights it had been through.
They also happened to simultaneously have some of the largest bounties in the Empire on their heads from several Hutts, the Empire, and the Rebellion at the same time...
Huh, which makes me think of the Alternity game back in the day where one of the PCs, Ty Scrawj, got beat to hell at a crummy stardock bar, came back with his auto-flechette shotgun, climbed up on the bar to reap bloody vengeance, and accidentally hit the clip release after trash-talking everyone in the place.
He got knocked off the bar by taking a sledgehammer to the chest and after the other PCs found, rescued, and escaped with him, the only doctor they could find to patch him up was a junky chop-shop doc who demanded drugs in payment, then took them right before he operated on Ty. Amazingly, Ty lived, though for some reason he set off metal detectors after that - which caused more shenanigans later.
Edit: Oh, as a final note, one player was at the 2nd Edition game, his first time roleplaying ever and his first day in town after moving across the country (he was one of my player's cousins), when they took on a black dragon. The party spread out, wise (by then) to breath weapons. The player had to leave, right after he took his turn and the wizard hid behind his PC, hoping it would ablate the dragon's acid a bit. Instead, the dragon melted both of them to a puddle. One of the players grabbed the new player's character sheet, tore it up, and lit it on fire with a lighter.
Next game when the player came back, I handed him the charred scraps of his character sheet. "What happened?" he said. "You got puddled," was my reply. His nickname was Puddle to everyone (including people at highschool who had no idea we roleplayed) from then on out. I haven't seen him in years, so as far as I know, it still may be - though I bet almost no-one knows why...