What’s the longest you will let a beverage sit and still drink it?

Generally my limit is same-day, though I often don’t drink something that’s been sitting for a few hours.

Rule 1: Check for bugs.

Will you drink it the next morning?
Maybe

What about the water the next night if there is still some left in the same glass?
No

Does it matter what beverage it is?
Yes.
Water I feel the least concerned about. But it’s also easily replaceable.
Beverages with milk/cream, or that I want to be a certain temperature, I give the least time.
Juices are somewhere in between.
Some wines are ok to open, leave out, and re-usable later, at least for a few days.

Does it matter if you already took a sip from the glass?
Yes, but it just adds a little bit to the consideration.

What if it’s a bottle of something you started. How long?
The bottle reduces the bug risk a lot. Especially with a lid. But otherwise it’s about like something left in a glass.

Does it matter if it’s kept in the fridge or at room temperature?
Very much so… unless it’s just water, or alcohol that’s meant to be left out.

Does it matter if you drank from the bottle?
Yes. Makes it worse.
Something I haven’t drunk from the bottle, re-lidded and put in the fridge, I’ll consider ok for several days.
If it’s in a sealed bottle, and I’m the only one who drank from it (which I only very rarely do unless I’m planning to drink it all and/or I’m sure no one else will drink from it), then I’ll consider that ok in the fridge for a few days, too.

Based on the radioactive isotope potassium 40 half-life of 1.251×10^9 years I’d recommend a 72 year old Macallan scotch with a cube of 2.7 million year old ice

I keep my water in a lidded cup next to my bed for about a week, my coffee in an insulated cup all day, When I have wine, I nearly always drink it within the hour.

As a bit of an aside, when I had my daycare I developed the practice of bagging up uneaten food and milk and putting it in the fridge against the idiot kid who would go home and tell Mom that I refused to serve them lunch. Everybody got lunch except for them.
It was astonishing how fast that left over food / milk went really bad.

If I’m thirsty I’ll drink an abandoned water bottle left for an unknown time in the park.

I don’t have a hard and fast rule but if it’s coffee or tea in a cup, I’ll drink it a few hours later. Water, overnight in a glass by the bed, maybe I’ll take a sip the next morning if I’m desperate but usually not. If it’s an opened bottle in the refrigerator, like Diet Coke, I will keep it until it’s finished. Same if the bottle is not refrigerated. If a smaller Diet Coke (like a 20 oz), I will cap it and drink it the next day, no problem.

Until it’s empty.