Growing trees from seed is certainly a rather unusual approach for gardening, especially when compared to a simple shopping trip at the nursery. Yet, although it may be a more protracted path to your own trees, for many species it is very worthwhile.
Tree seeds can be stone fruit cores or pomaceous fruit seeds, and both often require special treatment in order to be capable of germinating, because they have a hard and waterproof shell. In addition, usually a cold stratification is necessary, as in their natural habitats tree seeds rest over the winter, before they germinate and sprout the next year.
Especially nut trees, all kinds of non-grafted fruit trees, shrubs and hedges are excellent candidates for growing from seeds.