Generally yes, but not always. If you include the APU as an engine, the answer would need to be different, but I understand your question concerns just the engines used for propulsion.
For jets, the direction of rotation doesn't make much of a difference, so the same engines can be used on all stations. However, with propellers the swirl does influence flying characteristics, especially at low speed, so special left- and right turning versions of turboprop and piston engines are available.
Maintenance and logistics become much simpler if only one type of engine is used. In the past, not so much emphasis was placed on this, so some airplanes used different types of engines. Examples were:
- Convair B-36B, which combined piston and jet engines in the same airframe
- Junkers G-38, which used a Junkers L88 inboard and a Junkers L8 outboard. Later, the outboard engines were also changed to the L88. This can be seen from the number of propeller blades: If the outer engines drive a two-bladed propeller, it is the earlier version with the L8.
- Hawker-Siddeley Trident 3, which was almost a four-engined jet, because it had a small, tail-mounted RB-162 engine in addition to the three tail-mounted RB-163 Spey to provide thrust on takeoff.
- Rutan Voyager, which used a bigger front and a smaller rear engine.