As of question writing, all known life is carbon-based, in the sense that it needs to contain carbon atoms to survive.
But life could take many forms:
- Wikipedia has a handy list of hypothetical types of biochemistry, notably silicon biochemistry.
- Life could be based on non-organic chemistry (e.g. inorganic chemistry, or nuclear chemistry in the degenerate crust on the surface of a neutron star*).
- Life could also not be chemistry based at all. It could be electrical (e.g. Ems) or mechanical (e.g. clockwork).
- Life could operate on vastly different time / space scales from us (e.g. a cloud of interstellar stuff somehow consistently implementing a sentient computation).
These examples are not necessarily mutually exclusive, and I obviously make no claim regarding their respective feasibility/likelihood. They are rather meant to suggest the vastness of design-space.