To answer that question I can do no better than quote Christopher Lloyd from his great book 'Succession planting for adventurous gardeners':
'Self-sowing plants plug gaps with relaxed abandon and are a great help in keeping the show going, as long as you treat them as allies that need to be controlled'.
If you are a gardener who likes it all very, very neat, than they are probably not for you. But if, like me, you like a more relaxed and blousy kind of planting with no bare soil throughout the growing season then they are to be recommended.
The obvious easy candidate is the humble forget me not. Lovely in May to cover the ground under spring bulbs such as tulips and later daffodils. I saw a gorgeous, rich combinaiton at Great Dixter a couple of years ago: a deep, mauvey-pink forget me not with 'Red Shine' tulips. You absolutely could not ignore that planting!
Self sowers can form a kind of theme running through your borders to give a bit of continuity and gentle grace. Some of the plants we use for this are Welsh poppies in spring, opium poppies and alliums in early summer and Verbena bonariensis from late June onwards. They are all good mixers, provde valuable succession and, as long as we make sure they don't smother their neighbours, they add real charm and colour.
The best way of nurturing them is to get down to soil level on your knees with a trowel in early spring; if you thin them out fairly ruthlessly then they will have space to develop and do their thing. I try and leave around a foot in between forget me nots or they will quickly become congested and then mildewy. Biennuals such as foxgloves, verbascum and sweet williams are bigger and need more space, they take two years to germinate and flower so patience is required! Alliums self seed freely but can take a while for the bulbs to reach flowering size. We have them mingling with grasses where their tatty, pongy foliage disappears under the miscanthus leaves but the allium seedheads remain and look good for a month or more.
Bear in mind it's hard to make a garden entirely out of self sowers. Unless you are looking for a really chaotic meadow effect that is.
Photos from left to right: Allium christophii, opium poppy and sweet william all in flower here at 'Charnwood' at the end of June 2012