There are a group of plants which are known for their propensity to self seed around the garden with no effort by the gardener.
There are significant advantages to self seeding plants. It means you get new plants each year for free; it bulks up the garden stock of plants and it involves no effort. It is possible with some self seeding plants, to take the seed head when the seeds have formed, and shake it into the area of the garden you would like the self seeders to plant themselves and so have some control over where the self seeding plants grow.
There are also downsides. Some self seeders, such as Alchemilla mollis, are very vigorous and may self seed too much. This means to keep the plant in check you must either cut off the flowers before they run to seed, or dig up unwanted plantlets. There is not a lot of control over where the seeds land and germinate, and you may not be happy with the haphazard planting by nature. Taking all this on board below are short descriptions of some of the best self seeding plants.