The OP asked about automotive engines not just cars, so I’ll add some stuff about motorbikes. If I’ve missed anything, please feel free to add on.
Singles
Many motorbike manufacturers produce single cylinder bikes (usually for trail bikes)
Twins
Most major manufacturers produce a V-Twin engine and there are a few inline twins while BMW produces a flat boxer twin
Triples
Honda produced a v-triple (MVX250 from memory) that was a bit notorious for burning out the rear cylinder.
Triumph produces an inline triple (and other manufacturers have done so in the past).
Fours
The most common configuration for larger bikes is inline four (though the v-twins are gaining ground) and there are a couple of V-fours around (the Honda VFR comes to mind)
Sixes
From memory, the Honda Goldwing is a flat boxer 6 (and I think it might have been a Boxer four in the past)
There are or have also been inline 6s and v-sixes. The Kawazaki Z1300 being the prime example
Other oddities
Ariel once produced a Square Four (sometimes called the Squariel) that was also notorious for burning out the back two cylinders.
There have also in the past been numerous flat singles, flat boxers that go along the frame (instead of across)
The Munch Mammoth used a Volkswagen beetle engine
The ill-fated JPS Nortons used a rotary engine and Bombardier used to sell a rotary engne for going into other bikes.
I think DKW or one of the other German manufacturers experimented with a steam motorbike (or scooter) at one time.
To round it all off, I think the Orbital Engine produce by the Orbital Engine Company (aka Sarich) was used in a few motorbikes.