I'm a GA pilot and use the following.
BUMFISH for a downwind check. Note that it has to be adapted slightly to each type with common sense. "Fuel" could be on and sufficient, through to fuel pump on, fullest tank selected and quantity sufficient. "Instruments" includes engine and flight instruments.
Then I have a couple of pre-landing checks. Initially I was taught Mixture, Pitch, Gear (which has still stuck because I started with this check) but the more common one is PUF (Pitch, Undercarriage, flaps). You can make it PUFC if you are using carby heat in the circuit.
After landing and on taxiway I do FROST. Flaps Identified and raised, fuel pump off. Radios (frequency, call if required), Oil temps and pressures, switches (turn everything off that is not required - landing light, strobes, navaids) and SARTIME (cancel if required), Transponder to standby (and reset code to 1200/2000).
(By the way, BUMFISH is also a great pre emergency landing checklist, just think in terms of shutting down though - so undercarriage up or down as required, Mixture is idle cut off, fuel off, instruments could be ELT, all switches off, hatches cracked, harness secure etc).