The term "best fighter engine" is so vague as to be almost meaningless. Best in what way? Ability to survive damage? Least amount of maintenance required? Applicability to the greatest number of different types of aircraft? Actual use in the most different and different types of aircraft? Ability to be mass-produced? Available power for combat situations?
For me, the clear winner on ALL those categories is the P&W R-2800.
The R-2800 was legend for its ability to survive combat damage, with many, many stories of aircraft returning with cylinders hanging out a hole in the cowl and still chugging away. I'm on somewhat shakier ground on the amount of maintenance needed, but all U.S. radials were such that if they weren't leaking oil while sitting on the ground there was something seriously wrong with the engine. With ANY inline engine, one bullet in the wrong place would turn your sleek aircraft into a sleek brick headed toward the ground. The previous was a major reason that the P-47, for all its abilities as a fighter/escort, was moved so heavily into ground support in Europe and elsewhere.
As for the number of different types for which the engine was applicable, here is a list of only those that actually saw combat: B-26 Marauder; A-26 Invader; F6F; F4U; P-47; P-61. Many of the experimental fighters, attack aircraft and bombers were designed around the R-2800. And the F7F and the F8F were on the verge on combat when the war ended. the C-46 was also powered by the R-2800. Interestingly, the first B-32 off the production line was delivered with R-2800's with the thought that the later, high-powered methanol-injection versions were going to produce enough horsepower to push the aircraft in the combat requirements of the type - also because the R-2800 was a readily-available, highly-reliable and a well-known engine in all theaters. As such, the training regimens for maintenance and the logistics trail were also well-established.
The magnificent Merlin clearly meets many of the above criteria as well. However, its susceptibility to damage to the cooling system - to me at least - places it in a probable second place.
The United States had a tremendous lead in the design and production of radial engines. Much of this was due to the needs of commercial airlines who wanted light, powerful engines that were easy to maintain in the middle of nowhere. Up until the late 1930's the Army Air Corps was building its "fleet" around liquid-powered engines - especially the Allison the later into the 1930's you get. However, several important reports - the Kilner and Emmons boards - essentially stated that the U.S. was in dangerous territory putting all its eggs in one engine basket. At this point much greater emphasis was placed on higher-powered radials as well as more serious developmental work on the so-called "hyper engines."
I'd like to suggest that in such future questions a massive degree of additional specificity be part of the query. Otherwise we end up with questions that sound like "What color blue is the best?"
Respectfully submitted.
AlanG