With the best will in the world, problems do occur. There can be few gardens, for example, where slugs are not a nuisance, especially in early spring when the succulent shoots are first appearing.
You can, of course, try to use only slug proof plants, but when slugs are hungry they will eat most plants, so if you remove their favorite food, their tastes are likely to change. You can use slug bait if you are careful to ensure that pets and other animals cannot get at either the bait or the slugs once they have eaten eat.
One of the best methods for getting rid of slugs is to go out in the evening as it gets dark with a torch and collect the emerging slugs in a bucket and dispose of them at some distance.
Do not throw them over your neighbor's fence as they will just crawl back and your neighbor will not be best pleased. After a few nights, you will have reduced the population sufficiently so that they are no longer a problem, at least for a while.
Caterpillars can also be removed by hand. Rabbits are another big problem in some gardens. Here the only real solution is to place a rabbit proof fence around the whole garden.
You could just fence off individual borders, but the fencing does look ugly and is less obtrusive if placed around the whole boundary.
Small outbreaks or aphids can be left to other predators to deal with, but if they begin to accumulate you can remove them either by running your fingers up the stems and squashing them or by simply removing the stem.
Greenfly and black fly are common pests. A mixed garden will usually provide sufficient predator insects to combat them.