Extracted from the website of Buddhist Vajrayana Charity Funds Association and translated (可以殺死蚊蠅蜂蟻蟑螂等蟲類嗎) into English:

Can we kill insects, such as mosquitoes, flies, bees, ants, cockroaches?

【Dhammapada】 (【法句經】) said: ‘All sentient beings fear death, none is unafraid of sword and cane, put oneself in other's situation, do not kill and do not use cane.’ From this point of view, there is absolutely no way to remedy the tragic results created by killing, because the most precious matter in the world is life. Amongst every single sentient being, there is not one that would not appreciate living and love life.

【Brahmajala Sutra】 (【梵網經】) said: ‘All those who have life, cannot be killed.’ This means one should not kill any living creature.

Compassion is the foundation of Buddha Dharma, and to refrain from killing is compassion. In the Ming Dynasty, the 《Release to Freedom Essay》(《放生文》) written by Lotus Pond Master (蓮池大師), has this profound description: ‘Having heard that in the world life is most important, the greatest tragedy in the world is killing and harming, hence all will run for life whenever captured; lice know how to avoid death, and migrate whenever it rains. Since ants greed for life and are afraid of death, why humans still set nets/traps for hunting animals in the mountains and use fishing nets for catching fish in deep water? Why do people use various ways and think everything possible to catch living creatures? They either use hooks, bows and arrows to capture or shoot animals, causing them tremble with fear and are scared out of their wits (frightened to death). Families break up as children are separated from their mothers. The captured animals are like prisoners who are put into jail whereas the animals on the chopping boards are like the criminals who are going to be put to death in the execution places. A deer mother, which licks the abscess-scar of its baby deer, feels too sorrow as if its intestine is broken into inches by inches. An ape, which is afraid of death, seeing the sharpshooter pull the bow, can’t help but weep with two lines of teardrops (waiting to be shoot dead). People think they are strong to bully those weak animals. I’m afraid this concept is unsuitable.’

Can Buddhists kill mosquitoes, flies, bees, ants, cockroaches and other insects? We, Buddhists, must never at any time tamper or change the Buddha's original meaning. Righteous Buddhists should be comparatively clear about the precepts against killing. When one initially learnt Buddhism, one would have been told not to kill living things, including mosquitoes, flies, bees, ants, cockroaches and other insects should not be harmed. The following are some case studies on some Exoteric and Esoteric eminent monks and patriarchs who protected lives and the retribution to those who killed:
●	Whilst the Great Master Hsu Yun (虛雲大師) and the Buddhist patriarchs of the virtuous of successive dynasties worked hard in the field, they were never seen to have used insecticide, and there were definitely no pests that could have been seen running rampant! Those who encountered pests in the farmland could be have been considered as having insufficient blessed reward. If they further created the karma of killing, then it would have been even more unworthy. The old monk Hsu Yun never rashly showed his miraculous power, and he would not allow his disciples and followers to randomly show off their miraculous power either. During the lifetime of this Great Master Hsu Yun the maximum number of times he manifested his miraculous power was: walking without touching the ground, as he was, in actual fact, flying. Often, he would display this miraculous power and when he was later discovered by one sharp-eyed disciple who asked for the reason, the Great Master Hsu Yun replied: “Not to injure ants and insects.”
●	Once, the Great Master Hsu Yun and Dharma Master Jie Chen (戒塵法師) stayed overnight in a small ruined uninhabited temple. In the middle of the night, a flea bit Dharma Master Jie Chen's body. He placed the flea on the floor. The flea fell onto the ground and broke its leg. The old monk (the Great Master Hsu Yun) heard the extent of the flea’s tragic scream during meditation. The next day the old monk questioned Dharma Master Jie Chen about this event. On hearing this, Dharma Master Jie Chen was very surprised and thought: “How could the Great Master even know that I placed a flea on the floor, moreover, he could hear the scream of the flea. The skill of his meditation must be outstanding!” From this, one knows that the realm of purity in body and mind is truly inconceivable; one can also see that when a small creature, like a flea, is physically injured, it also has the feeling of pain.
●	《A Guide to the Preliminaries of the Great Perfection》 ( 《大圓滿前行》 ) records: In the past, when the Emperor Lok Hang of India was a prince, in order to accede to the throne early, the prince requested Long Meng Bodhisattva (Dragon Mighty) to offer Long Meng’s head to him. The prince first used his stately sword to chop his neck, but it was like chopping into air, not a single injury was inflicted. Long Meng Bodhisattva told him that his karma of weapons was eliminated, except when he had once cut grass in the past he killed an insect and this debt had not been repaid. Hence, only the auspicious grass could chop his head off. Later, what he said came true. Source of Information: 《A Guide to the Preliminaries of the Great Perfection》 and 《Great Tang Records on the Western Regions》 both record this historical record as “Long Meng” Bodhisattva. However, other research materials showed that “Long Meng” and “Long Shu” (Dragon Tree) are the same person, 《The Great Tang Records on the Western Regions》Volume 8:「South India Nagarjuua Bodhisattva (Chinese text as Long Meng. Old translation known as Long Shu).......... 」, 《Letter of Relatives and Friends of Long Shu》、The History of Indian Buddhism and other books.
●	When the Tantric Great Perfection Lineage Ancestral Master Benzuo Zana was a monk in his previous life, he had once killed lice on his body. Due to such karma, after being moved to the place called “蔣慕茶瓦容” he was imprisioned in a prison full of lice.
On 16th June 2009, when the American President Obama was having an interview with CNBC television morning news in the White House, a fly kept flying around in front of his face, and it ultimately landed on the back of his left hand. He could not tolerate the disturbance so he raised his right hand and slapped it to death. This act created strong discontentment from numerous animal protection organisations. On 22nd June 2010, when President Obama was delivering his speech at the East Wing of the White House, another fly flew back and forth in front of his face; for a moment it stopped on his head, then it stationed at the corner of his eye, then on his cheek, then it rested on his nose, and even once, managed successfully to “settle down” on his lips. Obama was interrupted a few times during the speech, and used his hand to drive the fly away, but having learnt the lesson from last time, and he did not kill mercilessly.
Some people say that by killing flies and insects, they are helping to remove their karma, to enable them to leave the evil path as soon as possible. Yet, isn’t this merely a self-satisfying statement? So, would you allow someone to kill you, to enable you to quickly eliminate karma and reincarnate? You most certainly would not be willing. There are even people who, when they see ants, cockroaches and rats, chant “Buddha Amitabha” on the one hand, and kill the insects on the other hand, using flowery terminology to justify, “We are here to save them”. This type of action is totally incompatible with Buddhist theory. Basically speaking, the act of “Salvation” (超度) in Buddhism is to “benefit” sentient beings and chanting The Buddha's name for sentient beings is to wish them well. If you want to be kind to those small animals and insects, why kill them after chanting The Buddha's name? Suppose other people chant “Buddha Amitabha” once and then kill you, how would you feel? Would you be inclined for others to use this method to “deliver you to salvation” quickly? You most certainly would not be willing. So then, would mosquitoes, flies, bees, ants, cockroaches and similar insects be willing? Have you asked them whether they are willing or not? Therefore, one cannot belittle the life of any small sized insects. Everyone may wish to think about it.