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How many people have the power to wield Mjolnir?
I know of 5:
Odin
Thor
Hela (aside from stopping it, there is a painting of her holding it in the "great hall" when she unveils the covered ceiling)
Vision
Captain America
Is there anybody else who has picked up Thor's hammer?
Technically anyone pre-Thor, so pre-2011, would have been able to wield Mjolnir as the worthiness enchantment was only placed on it then. However, as we only get a very brief glimpse of this time period we don't actually see anyone else wield Mjolnir.
Odin: Whosoever holds this hammer, if he be worthy, shall possess the power of Thor.
Thor, Mjolnir's enchantment
Onto those we've actually seen wield it though.
Obviously Thor wields Mjolnir and although he temporarily loses the ability to wield Mjolnir in Thor, he becomes worthy again at the end of the film.
He can clearly be seen wielding Mjolnir, he does so when he banishes Thor and actually can still wield it after he places the enchantment upon it, so he is clearly also worthy of Mjolnir... which makes sense since he placed the enchantment.
When Vision first comes to be he held Mjolnir straight away and passed it back to Thor. To be 100% clear on if he "wields" it though we see in the battle against all of Ultron that he does use the hammer.
However, as Steve and Tony note it is possible that because Vision is artificial "different rules" apply - though he is part living tissue.
Steve Rogers: The rules have changed.
Tony Stark: We're dealing with something new.
Steve Rogers: Well, the Vision's artificial intelligence.
Tony Stark: A machine.
Steve Rogers: So it doesn't count.
Tony Stark: No. It's not like a person lifting the hammer.
Steve Rogers: Right. Different rules for us.
Tony Stark: Nice guy, but artificial.
Steve Rogers: Thank you.
Thor: If he can wield the hammer, he can keep the Mind Stone. It's safe with the Vision and these days, safe is in short supply.
Steve Rogers: But if you put the hammer in an elevator...
Tony Stark: It would still go up.
Steve Rogers: Elevator's not worthy.
Avengers: Age of Ultron
As we see in Thor: Ragnarok Hela can stop Mjolnir in its tracks even with the enchantment on it. This is more likely to do with her own powers rather than her being worthy though of course because she doesn't act worthy. Although as we see on the mural she actually wielded Mjolnir in the past before Thor's time when conquering the Realms with Odin.
Click images to enlarge.
He was always worthy, ever since the scene in Avengers: Age of Ultron where we see him move the hammer just a nudge, however, he chose not to pick it up. See this answer of mine to a related question for evidence on that. However, we don't actually see him wield Mjolnir until the Battle of Earth in Avengers: Endgame where he picks it up to fight Thanos.
Lastly, I think it is worth noting that Jane Foster is set to reappear in Thor: Love and Thunder (2021) as Thor and so it is possible she will also wield Mjolnir. It was even teased that this would be the case in the reveal at San Diego Comic-Con where she took the stage with Mjolnir in hand. Whilst this isn't conclusive proof as there are no set pics or footage released yet it is a strong indicator Jane Foster will also wield Mjolnir.
Click image to enlarge.
On a slightly different note the upcoming Disney+ series What If...? has had the first episode revealed to be about what if Peggy Carter had taken the super soldier serum and not Steve Rogers. Whilst it's not entirely clear what this will entail, if it shows Peggy in the "future" as Captain America we might see her wielding Mjolnir. Although of course this isn't the main MCU continuity so shouldn't be taken as such.
As the querent indicated that they're interested in the comics continuity as well as the MCU, I've quoted the list from Wikipedia:
