From my understanding, many of the features of water that make it very important for Earth's ecosystem are a result of oxygen's high electronegativity, which results in hydrogen bonding.
As nitrogen and fluorine also have some similar properties (High electronegativity, hydrogen bonding, stable hydrides, etc.), could they serve the same role water does in an alien ecosystem? (Obviously under different temperature and pressure conditions)
(I was directed to here from biology)
The book Xenology has a section about alternatives to water, and this boiling point calculator helps show the variance due to pressure.
Now, in my estimation, life will use whatever is the easiest in its current conditions. The reason why terrestrial life uses water is because most of the planet is not boiling or freezing (currently). In order for life to prefer ammonia or hydrogen fluoride instead, it would have to be perpetually in conditions where water is never available in liquid form.
Ammonia and hydrogen fluoride have boiling points around the freezing point of water, all at one atmosphere. Increasing the pressure will increase the liquidity range, roughly speaking. So an ice planet is probably the most likely to harbor ammonia or HF-based life.
Above the boiling point of water you are better off using something like sulfuric acid. Curiously enough, acids lose their acidic properties in environments devoid of liquid water.
Water is important for life not only for the factors you listed, but also because:
Just to give you a measure of how these properties impact life, note that upon freezing ice floats on water, with the maximum density being achieved at around 4 degrees.
If that wouldn't be the case, ice would sink into the water, with the obvious result that any water body in winter would totally freeze.
Also the high specific heat allows water to be that important for mitigating climate next to large bodies of water.
As far as I know, ammonia and HF do not have the same behavior, that's why it is more difficult to base life on those.
Ammonia has some impressive properties as a solvent, including solvating metals (sodium, potassium, aluminum). It's true that ammonia ice doesn't float, but...
Many discussions of this question seem fixated on water's particular set of properties (expansion on freezing, acid/base balance, etc.). These strike me as Earth-chauvinism. I can just as easily imagine an ammonia-based race dismissing water as a basis for life. "Too hot (denatures proteins before it even boils)! Too acid! Too chemically limited (only two instead of three hydrogens)! And cells would rupture every time they froze!"
HOWEVER, I notice that the last few decades have brought us news of numerous water worldlets (Jovian moons, possibly even Ceres), but not much about worlds that could bear ammonia oceans. It may be that water life wins from simple abundance.
One good science-fiction read on the topic: Still River by Hal Clement.
