Well for life to be on "every" planet you'd need life that can survive on bare rock without air, or in lava, etc., so it would be quite bizarre from our perspective. As I see it, life of any sort absolutely must have the following two resources:
1: a solvent in which the necessary molecules for life processes can be dissolved so that they can move around and recombine. On Earth this function is served by water, but any liquid that dissolves a sufficient quantity of a sufficiently wide range of molecules may suffice (e.g. ammonia).
2: A strong energy gradient--on Earth this is sunlight coming down from the sky, giving energy to be absorbed, but on a planet with strong geothermal energy and little sunlight (and thus a cold sky), plants might run a heat engine that takes heat from the ground and radiates its waste heat into the sky. It is imaginable that a world with lots of radioactive isotopes might develop life that concentrates these isotopes for energy (radiation-eating fungi have been discovered in the ruins of the Chernobyl reactor). However, life that merely eats non-renewable chemicals in its environment will eventually deplete them over billion-year time scales.
Beyond these two things, the details of biochemistry are fairly flexible in theory.
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