Especially on higher levels (Emperor+) everyone will be annoyed with you as long as you don't have an embassy. [/Lanzelot]
Depends on the aggression level, how much you've traded them luxes, techs, resources, gpt, and lump sums. Pretty sure I've had a few games where I haven't had embassies, and polite tribes in the middle ages, but with least aggressive AI and some tech trading also. Still, I agree that embassies make a significant difference.