Many vegetables, including tomatoes and runner beans, can be started off indoors. Some, like celeriac, need a long growing season to bulk up, so are best started off indoors rather than direct outdoor sowing. See RHS Grow Your Own for advice on growing specific vegetable crops.
Annual bedding plants, such as morning glory (Ipomoea), sweet pea (Lathyrus odoratus), marigolds (Calendula and Tagetes species) and sunflowers (Helianthus cultivars) can be started off indoors to create flower displays for the summer.
Some tender perennials, such as cannas, begonias and Diascia can also be sown from seed indoors, but generally take two years to reach flowering size. Perennials live indefinitely, so a slow start pays off in the long run!