Much of the time, the novels don't specify exact figures - 'heavy burns' are referenced without further detail. That said, there are some clues in odd passages of text.
There are several factors to consider. With the Epstein Drive, continuous thrust is possible - higher thrust leads to shorter travel times (as discussed in the comments), but is both less fuel efficient, and less comfortable. For crews that will plan on returning to a planet, maintaining their ability to cope with the surface gravity is an added incentive.
Further details below, but as an outline:
Belter ships (or with Belters on board), 1/3g for normal civilian burns seems typical.
Martian civilian ships likely run at about 0.4g; military crews routinely train at 1g - unclear if this is a normal burn, or interspersed with 0.4g runs.
Earth civilian ships up to 1g.
In an emergency, higher burns were known - civilian ships would rarely go to 2g, but could manage higher; capital ships appeared to generally top out around 8-10g, without much difference between origin - even Belters (if trained, and on the juice) could survive this acceleration for a while; smaller ships like the Rocinante could hit 15-20g - although using this power was almost unheard of.
Laconia developed technology to go to 30g, but it wasn't much fun and not routinely used.
Specific examples:
Canterbury, with mixed crew, 1/3 g in Leviathan Wakes:
Holden knelt beside her chair. In the one-third g of their current thrust, it was perfectly comfortable. (Leviathan Wakes, Chapter 1)
Two g for a civilian crew was manageable but uncomfortable; they would go higher in a true emergency however:
Ten minutes at two g, and Holden’s head was already starting to ache.
[...]
The thrust suddenly dropped to a tolerable two g and all the ship’s sensors flared into overload. (Leviathan Wakes, Chapter 5)
The Rocinante (still the Tachi at this point) hits 12 g - Alex was military trained, but still a Civilian pilot at this point:
The hole had been punched out by a jagged end of Amos’ broken tibia when the suit had pushed against it at twelve g. (Leviathan Wakes, Chapter 9)
Theoretical maximum was higher - with doubts that the crew could manage it:
The actual limit was one of those trivial numbers, a way to brag about something your ship would never really do. Fifteen g, was it? Twenty? (Leviathan Wakes, Chapter 51)
Martian civilians find a 1g burn uncomfortable, but the military routinely train in it:
The Dae-Jung’s captain was being pressured by the diplomats to get them to Earth as quickly as possible, so the ship was running at a near-constant one g acceleration. While this made most of the Martian civilians uncomfortable, it suited Bobbie just fine. The corps trained at high g all the time and did lengthy endurance drills at one g at least once a month. (Caliban's War, Chapter 8)
The civilian ship sent by RCE to New Terra/Ilus used a sustained 1 g burn:
I mean apart from burning at a full g. (Cibola Burn, Chapter 2)
For Martian capital ships, 8-10 g was described as top end:
“Eight to ten g to start, curving down, which means they’re running at the limit of their drives.” (Nemesis Games, Chapter 28)
Recognising that speed is not the same as acceleration, it is implied that trained Belter ships can go match fairly hard burns by others:
Eight gs, maybe? Maybe more.
[...]
The two ships were bearing down on the Roci, pushing hard to narrow the distance. She didn’t know if that was bold or foolhardy. Probably they didn’t either. Ships full of Belters weren’t known for loving high-g burns, but this was war. (Babylon's Ashes, Chapter 27)
Laconia can manage 30g with a liquid buoyed crash couch, which was entirely outside any other (survivable) burn:
Surviving a sustained thirty-g burn in a conventional crash couch would have been about as likely as living through a free fall drop from orbit onto a pile of knives. (Tiamat's Wrath, Chapter 19)
