Peeves the poltergeist very rarely takes commands from anyone. However, he does listen to the Bloody Baron. What's the story behind this?
Let me summarize some of what we know about Peeves.
We learn that the Baron is the only one who can really control Peeves in Philosopher's Stone chapter 7, when we first meet Peeves, and Percy Weasley says
‘You want to watch out for Peeves,’ said Percy, as they set off again. ‘The Bloody Baron's the only one who can control him, he won't even listen to us Prefects. […]’
This later becomes a plot point: in PS chapter 16, Peeves catches the trio under the Invisibility Cloak, but Harry gets rid of him by pretending to be the Bloody Baron. Peeves is apparently terrified of having insulted the Baron (“almost fell out of the air in shock”), and leaves.
We know Peeves cooperates with Filch to catch students out of bed, and with the Weasley twins to wreak havoc in the castle and annoy Umbridge, but he does this in his own interest, enjoying what he does, and isn't actually controlled by Filch or the Weasleys.
Professors like McGonagall and Lupin and probably Dumbledore do sometimes have some authority over Peeves, see eg. PS. chapter 9 when McGonagall orders Peeves out of a room. This could be because they are powerful enough magic users to do magic on Peeves if he doesn't obey. Also, Peeves is very connected to Hogwarts, as we can see in Deathly Hallows, so that might be why he respects the authority figures of Hogwarts somewhat. Peeves thus tries to mostly stay out of their ways unless necessary, but it doesn't look like he's as terrified of them or respectful to them as he is to the Baron.
In PS chapter 7, the House ghosts are arguing about Peeves, mentioning things like “haven't we given Peeves all the chances he deserves?” and that “he gives us a bad name.” I think there's a possibility that any ghost has some way to interact with Peeves and control him more easily than the students, and the Baron just uses this in the most skilled way among the ghost, or is the only really terrifying personality among them.
Now a few facts about the Baron. We know his story. In short, he was a liege of the Hogwarts founder Rowena Ravenclaw, and the lover of her daughter Helena. Rowena Ravenclaw had sent him after Helena, who wouldn't return with him, so the Baron killed the girl in a rage, then committed suicide. As a ghost, he wears the chains and the blood as penance.
We don't know everything though, as the story doesn't explain why he became the Slytherin house ghost if he was a liege of Ravenclaw. (The Grey Lady is Helena, the daughter of Ravenclaw, and the Fat Friar claims that Hufflepuff was his former house, which explains how they got associated with their houses.)