Unlike diseases, there are fewer things you can do to minimise insect pests affecting your roses. You can't buy 'insect resistant' roses and it's harder to control the environment around them.
The most common insect pest of roses is aphids which affect a range of plants apart from roses. Aphids are those small green insects that appear in spring on the growth and can rapidly multiply. Small infestations do not cause much damage, its only heavier infestations which can stunt growth as aphids are sap suckers.
Small numbers can be dealt with your fingers; it's a bit gruesome but the best and easiest way to deal with them. Also encouraging birdlife around your roses can help – I've often noticed the silver eyes having a great feed on mine. I've also noticed that certain roses seem more 'palatable' than others and I have on the odd occasion, removed a rose that seems to be far more prone than the rest.
For heavier infestations, chemical control is pretty much your only option for aphids and you may have to follow up with another spray as eggs may have hatched since your first spray.
Mites are another problem, particularly when we get a hot, dry summer like the last one we had. The underside of the leaves are a silvery yellow colour with fine webbing present while the top side can have a brown-yellow appearance to them. A heavy infestation will defoliate your plants.
You can prevent mites by keeping your plants well watered and even on occasion wetting the leaves as they hate this. Just bear in mind wet foliage can cause problems like black spot so only do when it has a good chance of drying before nightfall. Also, avoid growing roses against things like tin fences and concrete paths, more so for smaller roses as the extra heat only encourages them more.
Winter clean up sprays help to control any mites still lurking otherwise they can be difficult to control once they get fully going.
Scale is another problem that can appear on your roses, particularly on the older growth. The scale lives as an immobile insect under a hard white coating and will suck the sap. Oil as a winter clean up spray can help control scale on your roses.
Other insects than can affect your roses include caterpillars, beetles, weevils and leaf rollers. These are not common but you may see them from time to time. Control is usually by chemical methods, consult with your local garden centre, hardware store or rose society for recommendations. Not that I am advocating chemical spraying as the only option for control, there are a wide range of controls out there that you can use but spraying may be your best bet if things are out of control. Also, if you do go down the spraying path, please alter which ones you use as resistance can build up in insects much more quickly than with diseases.
And finally and most important, take the proper precautions when spraying – always read the label and seek advice if required.