The fundamental thing about life as we know it is not just that it's made of the few particular elements it uses. It's about those elements being a sweet spot for molecular nanomachinery. It's not clear that any other combination of elements might be able to form a stable replicator and bootstrap itself into large-scale complex system. In fact, it might be that life can only arise by itself using materials our life is made of, directly because of laws of physics in our universe.
Or put in another way - if abiogenesis of our life is improbable, a spontaneous creation of robots - large scale machines with digital brains - is orders of magnitude less likely still.
It could be on the surface on active star, neutron star (someone already tackled that in sci-fi), all kinds of dwarfs, nebulas, maybe even something living off dark energy? Or black hole.
Energy means movement, and if matter/energy will eventually arrange into something 'alive', it might be enough.
• Hive-mind species where there are no individuals.
• Species without any gender or sexual reproduction, whose individuals are spontaneously "born" in specific locations and conditions on their planet.
• "Species" consisting of a single, massive/long-lived individual.
• Parasitic intelligences that "infect" various other, unrelated species and direct them towards the goals of the parasites.
• Lifeforms floating around in gas giants or even in nebulas.
• Life-bearing planets themselves being a lifeform; that "reproduces" when the civilizations it supported upon itself go on to terraform other planets to become like their home planet.