Similar to the Anakin = DV thread from a few weeks back, who exactly was likely to be aware of Palpatine's true identity as Sidious?
In the OT...Obi-Wan, Yoda, Luke, and Vader. Possibly Tarkin. I doubt anyone else did, though. Edit: Mon Mothma as well.
If we are to include prequel continuity, Bail Organa knew, so it is likely that his daughter and the rest of the rebels were aware of it too. It would be a strange thing to keep to yourself.
I wasn't really counting Bail as we don't see him in the OT, and he dies before he has any chance to influence the story. Strictly speaking, it's rather irrelevant to the Rebel cause whether or not Palpatine is a Sith Lord. That he's a military dictator whose underlings casually commit atrocities in his name is plenty
I never got the impression that the general public was all that educated on Sith Lords and I doubt Palp/Sid ever really demonstrated his force power for the masses. I doubt anyone saw him with a lightsaber.
Well it seems like he's got a whole entourage of shady, devious, corrupt politicians who are in on all his schemes, like Mas Amedda for example. Any number of them could have been in on the sith secret, or obliviously complicit. Wookieepedia says those two guys in purple pope-looking robes in Return of the Jedi are actually dark side adepts. I'm not much of an EU guy so I had no idea.
Movie-wise, the 'Imperial Dignitaries' were never meant to be Force adepts, they were just sycophantic lackeys in the Emperor's court (think Littlefinger from GoT, or maybe Wormtongue in LOTR, but with far less influence or power - Palpatine wasn't one to be manipulated by ANYONE). One, however, was apparently meant to be the same character who appeared in a couple of earlier drafts of ESB: This may or may not have been shot (probably not), but it was ultimately cut, and re-interpreted in the Rough Draft of ROTJ, where it is Jerjerrod who communicates with Vader. Some more info here: http://www.starwarz.com/tbone/minions-of-the-empire/ Pretty sure the official word is that he's the second from the right in this publicity shot, although various sources identify him as the first on the right: I do agree that such members of the Royal Court would have known Palps was a Sith Lord.
I doubt Vader or Palpatine would let Tarkin in on his true identity. All he seems to know in ANH is that Vader was once a Jedi.
It wasn't exactly a revelation like "I am your father", but it was still fun seeing Palpatine go crazy on Mace Windu before heaving him out the window
I doubt he would have consciously revealed it to anyone because it'd threaten his power. I imagine that at this point in the Star Wars universe, there would have been a search system far more powerful than our internet, with which one could simply type in the key words 'dark magical powers' or 'dark forces' etc and come across the Sith in no time, that is, assuming Sidious wouldn't have erased all documented history of the Jedi and Sith. This, however, is unlikely because he allowed the Jedi Temple to remain standing, I think he even gave people tours around it (EU), so clearly people would have known at least about the Jedi.