In this post, I'm talking about engines slightly abstractly, using "pump" to mean the entire pumping complex or "powerhead", which might be made of multiple actual turbopumps, and "combustion chamber" to mean the main combustion chamber, not any preburners or gas generators.
Most often you'll see one pump per combustion chamber and nozzle.
Some large engines, mostly Russian, split the combustion chamber: large chambers have more issues with combustion stability, while pumps appear to scale up more straightforwardly. The Soyuz's RD-107/108 engine comprises one turbopump and four combustion chambers + nozzles, for instance. The single-pump, four-chamber RD-170 used on Energia's liquid fueled boosters has 2-chamber (RD-180, used on Atlas V) and single-chamber (RD-191, used on Angara) derivatives using smaller pumps; these must have been very straightforward to design since the chambers and nozzles were already proven.
The first-generation Atlas rocket had a two-chamber booster stage; the design actually switched from a common turbopump to separate turbopumps and back to a common pump in various versions, which suggests that there isn't a huge advantage to one configuration over the other. The gas generator component was shared on all versions, which further complicates the counting.
The F-1 engine used on the Saturn V was large enough to run into these combustion stability problems, but they kept redesigning the injector and upper portion of combustion chamber until it worked, rather than redesign it as a multiple-chamber engine.
Saturn IB's H-1, Shuttle's SSME, Falcon's Merlin and the Electron's Rutherford engines are all one-pump-one-chamber engines used in clusters.
The pump's mass flow rate is essentially proportional to thrust. For a given pump rate, the engine is generally lighter if you're using a single chamber instead of multiple chambers. So from a thrust-to-weight standpoint, the ideal would be one big engine per stage: a single pump delivering the needed total thrust and a single combustion chamber.
In practice, there are several reasons to consider clustering smaller engines to reach the same total thrust: engine-out capability; throttling by turning off individual engines, and avoiding the engineering and logistics problems found in building gigantic single engines.