General rule 0.8mm for leaded parts and ICs, 1.0mm for 0.1" pin-headers etc.
You want at least 0.3mm above the lead size for easy insertion, but it isn't too critical and going bigger is rarely a problem unless tight alignment is important.
As well as lead dia itself, size of part, number of pins and likelihood of bent pins are other considerations - inserting a multi-pin part into close-fitting holes can be near impossible if there are misaligned pins - oversized holes make things a lot easier.
Minimizing the number of different sizes is also good as this can sometimes influence cost.
You spec the finished size - PCB maker will adjust for their plating thickness.