Is it forbidden in Islam to harm bugs intentionally?

Praise be to Allah, the Lord of the Worlds; and may His blessings and peace be upon our Prophet Muhammad and upon all his Family and Companions.

It is permissible to kill insects that usually harm human beings, like mosquitoes, bugs, flies, spiders, lice and the like.

However, the Prophet (Sallallahu Alaihi wa Sallam) forbade us to kill ants. Imam Ahmed and others reported that Ibn Abbas, may Allah be pleased with him, said: "The Prophet(Sallallahu Alaihi wa Sallam) forbade killing four animals: the ant, the bee, the hoopoe and the shrike"

However, it is permissible to kill ants that harm the person or his belongings like the white ants known as termites.

It is also permissible to kill the mouse or rat. The Prophet (Sallallahu Alaihi wa Sallam) said: "There are 5 animals which are noxious and should be killed outside or inside the sacred areas: a scorpion, a kite, a crow, a rat, and a biting dog. Reported by Bukhari and Muslim.

Allah knows best.