Chemistry places limits on what is possible. Water is a common and powerful catalyst, it is unlike any life can exits without it just because so many useful reactions happen only in water. (this discounts other catalysts mostly because they are not as common as water). Carbon forms long chains with single or double bonds (also triple bonds but they tend to be unstable) in ways that no other atom will. Note too that water and carbon are extremely common, so even if something else is possible you are then playing the odds that it is common enough.

I'm sure a real chemists can place other limits on what is possible.

Not a real chemist but my understanding is that there is no other solvent with all of water's properties - cohesion, adhesion, high specific heat, pH neutrality, polarity, density (in solid and liquid form), and reactivity - no matter how rare. It is the only "universal solvent" (for polar molecules). In order to imagine other forms of life, you'd have to make the jump from carbon to silicon based life forms. Unfortunately, the energies involved in the chemical bonds would mean that the reactions leading to self replicating molecules would have to happen at very high temperatures or densities which seem to make any life form extremely unlikely. Theoretically catalysts could lower the reaction thresholds enough for life to take hold, but it's an open question how such complex catalysts (enzymes) would emerge while bootstrapping replication. Earth went through just the right series of steps and until the planet cooled down, "stuff" just didn't stay in one place long enough to react and form big molecules.

The Miller–Urey experiment applied an energy gradient to a soup of water, methane, ammonia, and hydrogen.

This produced a smorgasbord of organic compounds, nearly all of which were the building blocks of life on Earth.

It's possible that applying energy to a different soup would produce different results - but all of the chemicals I listed are incredibly common across the universe.

Given that, if life exists somewhere else in the universe, it's incredibly likely that it will be quite similar, in chemical composition, to life on Earth.

I think there will certainly be differences in their DNA or RNA equivalents, but water will still be a nice solvent at room temperature and carbon still likes to form complex bonds and complex molecules at those same temperatures.

Thus at those temperatures and pressures as are found on earth, we can most likely expect to find water and carbon based life.

Will they have a carbon cycle? Certainly. Will it be exactly the same Krebs cycle, down to the exact same molecules? Maybe not.

Another critical property of water is that its solid form (ice) is less dense than its liquid form. This means that large bodies of water freeze on top and seal in a warmer liquid layer below. If not for this, then all lakes and even oceans would freeze solid. Most of the planet's water would be frozen solid year-round. Even during the "Snowball Earth" eras in our ancient past, only the surface of the Earth was frozen; there was still liquid ocean below. Very few compounds have this property of lower density when frozen.