Q:

Poker in the Star Trek universe: What are the stakes?

Obviously, when gambling with Ferengi or other aliens, the stakes are usually latinum. But on the Enterprise (or in Federation space in general), are they still playing for latinum, or are they betting chores (as seen in Firefly) or maybe holodeck time or replicator credits? I did a quick check on Memory Alpha, but it's not really spelled out what the poker players on the Enterprise-D are betting. I'm fairly sure they're not just playing for fun.
I'm asking about Star Trek in general, not just the poker games we see on TNG.

A:

In-Universe :
Since the Federation doesn't do money, the wagers are essentially meaningless. Play seems to be for the bragging rights as to who won or lost, the fun element of the game and the psychological focus on strategic thinking.
The exception to this in TNG is from the episode Quality of Life where Beverley Crusher taunts Will Riker into wagering his beard on the final outcome:

BEVERLY : Okay... what do you say we up the stakes a little? If I win
this hand... you all shave off your beards [and] if one of you wins --
I become a brunette. Are we on?
GEORDI : We'll take that bet.
n.b. script edited for brevity

And in the Voyager episode Collective :

NEELIX: I don't know what you're talking about. I've, I've, this is
the first time I've played. What is it called?
ALL: Poker.
PARIS: Look, why don't we make things a little more interesting.
Forget the chips. Let's bet on tomorrow's work detail, all right?
Whoever wins this hand gets the morning off.
CHAKOTAY: I'm in.

Mirroring Crusher in TNG, Paris says to forget the chips (which obviously have no worth) and offers a physical wager instead.

Out of universe
It's pretty clear that the actors and writers had no idea either. Despite the script constantly referencing Gene Roddenberry's assertion that the Federation is a 'post-scarcity' society with no money, the actress playing Deanna Troi (Marina Sirtis) clearly felt differently:

Generally, with most
beings, I could just sense what they were feeling, so I was empathic.
Why I was in the poker game, I will never know, because poker's about
sensing when people are bluffing, and there I was in a poker game
every week. I don't think you ever actually saw me win bundles of
money but I'm sure, off screen, at some point that was what I did.

as did showrunner Ronald D. Moore:

It is a strange platitude
that we used on the show, the need for money was gone and everything
was about bettering yourself. It was no longer about any kind of
material gain or personal gain, everyone was just trying to be a
better person So none of us could understand what that mean or how
that society functioned. It all seemed very vague. None of the writers
took it seriously. We all kind of laughed about it and joked about it.
We all had to pay homage to it because that was something that was
built into the structure of the show. At every opportunity we tried to
sneak in ways. How do you play poker if you don’t have currency? Again
The Original Series had credits and currency and we never understood
why they could do all these great things and we couldn’t. It was very
odd.

A:

Pride, favors, but mostly as fun or a mental/social exercise.  We see when Picard joins the game in "All Good Things" pt2 they just hand him a stack of chips with no discussion of buy in.  There also seems to be cross pollination of chips between games on the ship during "The Lower Decks" s7e15 when Ben takes his winnings from the Ensigns game to the Command Staff game.  It is implied that such "officers" games are common on Starfleet Vessels as Riker used it as a way to access the command staff socially on the "USS Potemkin".  We also have references of "favors" owed by other Federation Officers earned during card games peppered throughout the show.  Items like Romulan Ale, minor favors (covering shifts or doing undesirable duties), information, or favorable crew allotments are all things that Starfleet Officers will play for, including the shaving of beards (s6e09). 
We can assume there is some sort of Starfleet Regulation on gambling it's stakes, as gambling for too high stakes or with the wrong people can create security risks or threats to crew cohesion.  Within those limits groups of crew self organize pickup games or potentially shipwide competitions. It seems that on the Enterprise-D Riker is the main instigator of Poker (five card stud) and probably indirectly influences how the crew plays it and their standards for rules and fairness.

