Manbearcat
Legend
I typically have 3-4 players in games I run.
For me, it is the perfect number in play. Is enough for interesting interactions between characters and for non-trivial tactics in combat, but it gives a lot of spotlight time to each player. I run very character-driven games, so it is crucial that players are able to engage their arcs.
I have ran and played fun 1-on-1 sessions, so I think that the minimum number of players for me is 1. But I definitely prefer having 2 or 3 players.
As for the maximum number, I wouldn't go above 5-6, but even that is a lot. I would run a game for 5 or more players only if we agreed to never split the group and to reduce interpersonal interactions. While I have ran such games, that is not my preferred playstyle.
My players typically engage with their characters, situation and setting more than with the system. It's not that we ignore mechanics - we usually play by the book and avoid games with "rule zero" - but we mostly play games where the rules help focus on the fiction, not games where mechanics are fun by themselves.
I think that in my group I am the person who enjoys playing with mechanics the most.
I'm just going to ditto pretty much everything that steenan has here as it fits me almost word for word. I don't know if this is a point where we might differ, but my 3 players very, very much enjoy the mechanical side of games and 2 of the 3 definitely have well-developed opinions on various systems.
We're all very much inclined toward the heated pacing that I focus on as GM. They enjoy play being relentlessly pushed toward conflicts that they care about and they'd definitely rather push the pedal to the floor and put themselves in a spot, instead of turtling, to see what comes out of it. They're all comfortable with having plenty of authority at the table and they're smart, considerate, game-savvy, creative, proactive, and genre-aware, so I'm quite happy to give it to them.
Personally, I've GMed 1 on 1 and run many games with as many as 7 PCs (with a few at 8). While I can certainly enjoy a 1 on 1 game, anything more than 5 players is just too much (and most systems, not to mention play etiquette and GM overhead, break down pretty badly at that point). I've definitely found that 3, engaged, players is the sweet spot that I enjoy.