I recently sent two assassins after the PCs in my ongoing Thursday game, and it got me thinking about how best to approach this. Normally I start with the person hiring the assassin, think of who they would try to recruit and maybe make a roll to see, but otherwise just send that person or people after them (maybe in some instances I would make new NPCs for the job). But lately I am thinking more about coming up with an assassin hiring table for my NPCs, based on the NPCs level, reputation, social standing, wealth, etc. Just to give it a kind of random element.

Curious what people think is fair play when it comes to sending assassins after the party

I had assassins come after the players in a ToEE game (per the actual module). Even mid-level AD&D assassins can totally wreck a group of characters if you roll well enough. But honestly, that's to be expected because assassins in their element are badass. That said, I told them they were attacked in the night with assassination attempts and I let the players roll the dice to see what happened. I figured that if they had a change at insta-death, I'd at least let them do the deed.

For a game I was a player in, I had a pretty good half-orc assassin who had a really high CON and a lot of hit points, but he posed as a fighter (pretended to be poor so wore hide armor and had a beat-up shield, found a kickass magic sword, too). Anyway, shared game world the DM ran other groups in, they hired my character as a mercenary to assist with a delve into some crypts our group had already raided. I told the DM I was gonna sell them out and disguised as an ugly human fighter. After they paid my character his retainer, he killed their torch bearer in a dark alley, none of them had infravision, and he began shooting them with arrows while they were blind. A 5th level assassin almost took out 7+ characters of level 7-10; unfortunately only one went below zero and they all ended up making it out alive, but that group of PCs was scared shitless for a long time after.

So anyway, assassins are great if used properly.

Doppelgangers. Shapeshifting, mind-reading assassins who'll eat the PCs like trailmix.

I can't think of an occasion where I've specifically sent assassins after my players. Ambushes yes, but not the sniper/knife-in-the-dark style of specialist assassin. The occasion that pops into my mind was in my last 5e game.  I had a group of two demon-like creatures and an NPC monk attack my players in their apartment (it was an urban fantasy thing). But the baddies were mostly there to steal a mcguffin from the PCs and killing them was a secondary objective. Still, filling the room up with cloudkill and attacking them with monsters that were immune to it was pretty effective.

It's an interesting question. A good assassin doesn't let the target know they're being assassinated until it's too late, and definitely doesn't let them fight back. I think a skilled assassin would be unlikely to go after PCs with a standard sneak attack. Even the death attack ability gives a saving throw, and the assassin is going to be in serious dangerous if it fails. Even if it works, it only gets one target.

PCs travel constantly, so they're always meeting new people in unfamiliar places. It'd be pretty easy to get close enough to attack them indirectly with poison or traps. You could figure out an inn they're likely to stop at, pose as the staff and poison their beer. Or you could arrange to give them a booby-trapped item. Maybe a wand of fireballs which always goes off right at the feet of the caster. Since they're likely to use it in battle, it doesn't need to one-shot them, just soften them up for the monsters to finish the job. Or you could use the dungeon against them. Let get them to go into a crypt full of level-draining undead and then bar the doors behind them.

In game terms, I suspect those kind of indirect attacks, that instead of killing them outright, ratchet up the danger, are probably more fun for the players, too. "You're walking down the street and suddenly sprout a crossbow bolt out of your head" can feel a bit like "rocks fall, everybody dies". With the indirect attack, the players can figure out someone's after them, without knowing exactly who, and the assassins appear to still be competent. Yeah, it's a little unrealistic to give them any kind of a fighting chance, but it's better than having a couple guys in black robes jump out of the bushes so the players can carve them up.

I tend to play systems (or house rule systems) such that if you are unconscious and someone manages to get a knife to your throat, they can just kill you--no roll needed.  There may be a roll to get to that point.  Obviously, the situation has a huge effect on how difficult it is to get to that point and the parameters of any rolls. 

I also tend to not gloss over having someone on watch, that it is tiring, and that people need a certain amount of real rest.  This puts all such questions back on the players--gives them agency.  When the players decide that it is a bigger risk to not get rest than it is to double-down on watches, that's their decision.  If they do that after pissing some organization off bad enough that assassination attempts are likely, that's two different decisions compounding. 

IMO assassins as opponents is knocking on the door of "GM as adversary". I'm not saying they should never be used, but by definition, they are an opponent that attempts to beat the PCs specifically, preferably by the most underhanded and effective method possible.
And that can really suck to lose your character because he let his guard down that one time in an outhouse...

So I'd use them super sparingly, and be extra careful that the assassins (and their employers) are operating from NPC knowledge, and not GM knowledge.