Well, given that the definition is pretty much anyone who kills someone deliberately (and usually tries to get away alive) there’s a lot of room to make up whatever you want. History has many examples: for cults, there’s the Thuggee cult of India, for government-sponsored organisations, there are thousands (the WW2 Special Operations Executive was particularly well-organised and documented, but might be too recent). And then there’s ninjas, of course… I’ve never heard of a real “Thieves’ Guild” like the ones you get in fantasy games (they don’t seem like the sort of people who’d join a guild, to be honest) but maybe the crew of a pirate ship would work in a similar way: criminals, but with rules on how they’d work, who they’d attack and so on.
In terms of people working alone, you’d probably just hear about some dodgy bloke from a friend of a friend, meet him in a pub and give him some money. Also, it’s possible that hardened criminals wouldn’t call themselves assassins – they’d just consider killing people part of their job. Actually, as Thaddeus suggests, it would be good work for a vampire.