How far can a mosquito fly over the sea?
If we ignore the weather effects mentioned by Count Iblis we can do a fairly simple calculation.

The lifespan of a male mosquito is about 10 days whereas females live to about 50 days.

Their flying speed is generally about 1.2mph.

So if we assume that they can fly whilst asleep and maintain a constant velocity for their entire lifespan (obviously ridiculous because of the need to eat etc), their maximum ranges would be:

Male: 1.2 * 24 * 10 = 288 miles.

Female: 1.2 * 24 * 50 = 1440 miles.

It should be noted that these are absolute theoretical maximums. I would suspect real life values to be somewhere in the region of 10%-20% of these. However, once wind is taken into account they can easily spread globally.