All living things are eaten by other living things and your bonsai are no exception. 
A healthy tree will be able to shake off most diseases, keep it well fed use sharp tools to make cuts that will heal over better and you should have very few problems. 
Aphids, angelgids, mealy bug, red spider mite, and lopho (pine needle cast known as lophodermium pinastre) are all potential villains. If pests arrive, you have to fight them.
There are many available insecticides, each suitable for a specific insect and not necessarily suited for them all. Sometimes the first thing to try is to try picking or washing the insects off. A good rule to follow is to use the least dangerous method that will do the job. An insecticidal soap, for example, is very safe for humans, but must be rinsed off plants after spraying, as the fatty acids will eventually cover the pores on the leaves. It has to be sprayed fairly often, as it must contact the insect and has no residual effect. It must not be used on some plants (notably Serissa), so read labels. A chemically impregnated wax strip hung near the plant is worth trying for flying insects such as fungus gnats and whiteflies. It is quite safe for humans and indoor use but must be confined to a limited space. Contact insecticides will kill the insects they touch, or kill insects that eat or suck leaves the chemical is sprayed on. They are short-lived, which makes them reasonably safe for indoor use but they must be repeated regularly to be effective. These products will not kill insect eggs, so must be present when the larvae hatch from the eggs, to kill the next generation before they grow up and lay more eggs! Outdoor insecticides must not be used indoors. If an outdoor tree has an insect problem, an appropriate insecticide for that insect and that tree must be used. READ LABELS!
Some of the more common insects and appropriate methods of control :

Insects (in general) - The Type of insect taking an interest in your tree will vary with where you are in the world, however your response will tend to be the same. Man's ingenuity has provided us with chemicals to really put them off their lunch. Some of you will favour organic methods of growing your trees, however good these methods may be, their response time will not be prompt. 

Aphids - small, juicy-looking insects, usually light green, but can be white, black or grey, that suck sap from young leaves and flower buds. Most houseplant sprays will kill them on contact, but must be repeated every four to six days to be effective. Aphids produce live, female, pregnant aphids, so it is a challenge! Look for insecticides that contain Resmethrin or pyrethrin. Sometimes removing all the flowers and buds at the same time will make it easier to control them. Insecticidal soaps will only kill the aphids they come in contact with. Very careful watching for months will be necessary to be sure that a stray insect doesn't take over again.

White Flies - tiny white flies on the underside of the leaves that fly up into the air when disturbed. Sprays are not very effective, unless you can hit them when they are flying. Try a sticky yellow card near the plant, and shake the plant frequently to encourage them to fly to the card.



Red Spider Mite - If, in the joints between branches you see fine white cobwebs, you may have an infestation of red spider mite. They, as their name suggests look like spiders and make a web like substance. They're microscopic, just visible with a magnifying glass (look like very small, fine grains of white pepper on the underside of a leaf along the mid-vein). They tend to be associated with indoor trees, as they prefer a warm dry climate. Your local garden store should have something for them to drink (terminally), an insect killer will not work - it must be a mite killer containing Kelthane or Dicofol. It must be repeated once a week for several weeks, spraying the underside of the leaves. After that, spray (mist) your trees regularly with water, but have atention to the Humidity conditions. 

Fungus - I should start by saying that not all fungi are harmfull to your trees, all plants have a symbiotic root fungus called Mycorrhiza which benifits the tree. It can usually be seen as a thin white sheet around the roots, on repotting and is particularly noticable on Pines, it is as I said benificial. However most fungi will kill your tree, or disfigure the leaves. 
Fungi enter your tree through wounds and particularly those wounds below soil level, so when repotting your trees the first watering should contain a fungicide. Other fungi, such as mildew or blackspot will attack your leaves, disfiguring them and greatly reducing their ability to feed the tree, regular spraying with a fungicide will help to prevent this. 
Please note: when using any fungicide on a pine bonsai tree, do not allow the fungicide to get onto the soil, cover the soil with a polysheet or plastic bag and then a towel. Fungicide will damage the beneficial mycelium fungus that helps the bonsai pine roots to grow.

Fungus Gnats - tiny little black insects hovering around plants. The adults do no harm, but the larvae in the soil can damage fine root hairs if in large numbers. They prefer dying plant roots and are an indication that the soil is being kept too wet (which kills the roots). The plant may be watered too often, have poor drainage or be sitting in water. A soil dust will temporarily eliminate the problem but modifying watering habits will be the only way to completely eliminate them.

Powdery Mildew - is a fungus infection which is most prevalent in cool areas with high humidity. As this is common practice with some bonsai, it can be a problem. It looks like a dusting of fine icing sugar on the leaves and cause distortion and browning of the edges. It is controlled with a fungicide, such as Benomyl or Funginex. They are systemic fungicides which can be sprayed on the leaves and/or applied to the soil, as they are carried in the sap to the leaves. Warmer temperatures discourage mildew, but overwintering plants need cooler temperatures! 

Scale - looks like a drop of dried glue on the stems or undersides of smooth-leaved plants. It can be scraped off with a fingernail. There are no chemicals that will kill scale established on leaves or stems. The only one registered for use on scale is Sevin but it kills crawling larvae only, and they are rarely seen. It is possible to kill individual scales by rubbing each one off with rubbing alcohol, but this will not kill them all, and they will be back! It is better to eliminate that plant, as it can spread to other plants and is all but impossible to eradicate.

Scab - Scab is a disease commonly associated with Fruit trees. It is often seen in trees continually fed with high nitrogen feeds. It's unlikely to be seen in a bonsai fed with a well balanced fertiliser. 
High Nitrogen feeds promote rapid, soft growth and this, if damaged may allow scab to enter, so watch out. 
Scab itself is typified by the shrinking and drying of an area of bark. If you are the victim of such an attack you will find a remidy, usually a spray in your garden center. 
Assuming you’ve stopped the attack in time, you might consider applying a 'Dead wood' effect to the damaged area. 


If you are not sure what the problem is, do not spray to see if it will work! It is very easy to do more damage than the bugs could! Ask a knowledgeable person, read a book (preferably one with pictures of typical problems), or bring a leaf to a club meeting or a knowledgeable person at a garden centre. Be cautious with chemicals, and READ LABELS! 

Other Pests

Cats - Cats are not a problem if dealt with in a sympathetic and understanding manor. 

Little Helpers - The last thing I would suggest is that you keep you children away from your trees, however very young children will mimic their parents as part of the growing process. If they see you working on a tree they may decide to 'help' you, with perhaps disasterous results for your trees. Keep your tools away from them.