This depends on the mark and the role of the the particular Mosquito. Other answers here focus on its originally design role of a fast unarmed medium bomber, ignoring it was probably the most versatile plane produced by any nation in WW2. I won’t list them here but suffice it to say its uses ranged from high altitude photo reconnaissance, fighter and anti shipping attack with unguided rockets and torpedos.
As a night fighter it was rated by many as the finest of WW2, and its a shame RAF commanders restricted its use in this role.
The Germans were so in awe of it that they gave it two massive compliments. 1) They credited any pilot who shot one down with 2 kills. 2.) They tried to copy it with their own wooden nightfigher called imaginatively the Focke Wulf TA154 Moskito. Not regarded as a total success.
The final wartime versions were equipped with twin stage supercharged Merlins of over 1700 hp. These later versions had a refinement of the already streamlined, close fitting cowlings. Inspired by those of the North American Mustang with the supercharger intercooler inlet just behind and below the prop, the intercooler intake was moved to a similar position. They also had very sophisticated implementations of meredith effrect radiator ducting that was nearly as good as that of the Mustang. It was one of the few British planes the USAAF flew, used the reconnaissance role.
Depending on role these 30 series marks topped at between 415 and 425 mph. The NF Mk30 managed this speed with the encumbrance of a less than ideal radome nose and had a range without extra tanks of 1,800 miles.