Every Storyteller has a particular reason for why they run games. For some, it's a desire to share their cinematic vision of exciting battles and thrilling worlds. For others, it's an interest in a shared world where they can unleash their players upon a sandbox. Or they want to set an investigative puzzle spree like some slightly friendlier version of Jigsaw from the Saw movies. Some STs simply enjoy the social aspect of getting several friends to sit down, roll some dice, kill some werewolves, and indulge in some carnage.
Me, I like getting together a group of players with interesting characters and watching them interact. I'm like a really mean kid with a magnifying glass, some tweezers, and 4 - 6 different bugs to play with. I like seeing how they will interact with different NPCs and whether that will change as new information comes to light. I enjoy putting a puzzle before them and seeing if they'll engage with it or move away from it. I like smirking at their jokes, tempting them with their desires, and turning their worlds upside down. Rewarding them is fun as is seeing how they will react to their punishments.
In short, I'm a bit of a laboratory ST. I'm happiest when my players create deep and engaging characters with nuanced behaviors that are sympathetic enough to be likable but flawed enough to be interesting.
How about you? How do you get your ST jollies? Why do you run games?