Mosquitoes can mostly be ignored. They are rather difficult to hit successfully, and are incapable of dealing more than the slightest damage.
Mosquitoes will not attack players possessing the Insect Incense.
Mosquitoes offer almost nothing of value to the player. They may drop items, but their ability to evade attacks makes mosquitoes a poor choice for acquiring items. Note that they provide experience towards the next weapon level, which could make it worthwile killing them.
A variant of the mosquito, the Metal Mosquito, appears in the Greenhouse. It has higher attack power than the normal mosquito, but is otherwise statistically identical and is not much more of a threat.
In Ebon Keep dungeon, the top left cell, there is an event that can be triggered by trying to attack in a corner of the cell. the player will receive the message: "bitten by a Mazquito" and will be dealt 10% of current HP in damage. The player cannot be damaged under 1 HP however. This is a confirmed pun with Mosquito and one of the scenario scripters Paul Mazurek.