Meta -- these are generally my GM rulings and not subject to change:
1) No drow PCs.
2) Players have a right to contest a ruling, but the DM has a responsibility to keep things moving. If it takes much discussion, the ruling stands and we'll discuss between sessions.
3) No gender-bending. This isn't philosophic/political. Without exception, every player who did this was a misogynistic, socially maladjusted, sexually voyeuristic male, even when they appeared otherwise normal. I know that's not everyone, but I reached my limit years ago.
4) Gnomes dislike technology. They are forest pranksters. Lightning often smites gnomes who attempt anything mechanical or pseudo-mechanical. Instant death is a certainty if the attempt is even marginally comic. There are no exceptions. Ever. I won't even play at a table with a tinker gnome.
Defaults -- these may change if a published setting (Eberron, currently) has rules/assumptions to the contrary:
1) Elves have no souls. They have spirits that are reincarnated rather than going to an eternal reward/punishment.
2) Druids are animists. Even if they revere nature deities, their powers are derived from nature itself. This came up in 2E (at my table) as the defining difference between a Druid and a Specialty Priest of nature.
3) Clerics always serve one or more deities. If you want to serve a philosophy or ideal, go play a Psion (Mystic in 5E).
4) No halflings. They are bland and pointless. This goes here because of published settings that include them.
4b) Halflings are not kender. Kender only exist on Krynn. If your personality for your halfling is a tiny kleptomaniac, rule 4 stands. Unless we're playing Dragonlance; then, have at it.
5) It is physically impossible for gunpowder or internal combustion engines to function. Steam power is very unreliable, but might work as a one-off solution to a trap/puzzle if the player is clever.
6) Turn Undead is not available to all clerics. It's only for those whose deities have some sort of relationship to death or undeath. The Moradin doesn't see undead as any different than another foe. You're not channeling positive or negative energy (that's stupid) -- you're channeling the will of your god. (Eberron is a big exception, since the gods are remote.)
7) No construct PCs. (i.e. warforged stay on Eberron)
8) Critical hits are possible (house rule in some editions). Additionally, there's a chance for dismemberment or other significant bad things. I haven't updated for 5E, but we used to have a chance to role on the Rolemaster crit tables, which can be grizzly.
Explicitly allowed:
1) PvP: Not my first choice, but as long as no one has hurt feelings and fun is being had, I really don't care. Just stay in character while you're screwing the others over. When the fun wears off, though, we'll talk.
2) Evil PCs (evil players are still right out): If you play evil smartly, it tends to be pretty subtle and still interesting; I've actually played very fun evil characters who understood that mustache twirling draws way too much attention, but saw a contract to off the dainty elf maiden as being no worse than bringing back the head of the orc chieftain. If you're an idiot, though, you tend to die quickly so the problem solves itself. A couple of times, I've even assassinated a fellow evil PC because their scenery chewing was a liability. Also, no trying to destroy the world or create Hell on Earth -- that's where I keep all my stuff.