Pretty much everything is on the table, as an orbital environment puts little restrictions on what can work. So for an extensive list, wikipedia - spacecraft propulsion has a handy table. While most of them can be used, sort by technology readiness level for a more realistic view of what's available.
For most practical use cases outside mere technology demonstrations, there are:
- Simple cold gas thrusters.
- Chemical engines: monopropellants, bipropellants and solid fuel all used.
- Electric thrusters: electrostatic and Hall effect.
Common types of engines you will Not find in orbit:
- Jet engines, due to the lack of atmosphere, though ion engines taking advantage of the imperfect vacuum of low orbit has been proposed.
- Large powerful first stage engines, as their power are wasted on the very modestly sized payload we can currently get into orbit.