Different sorts of exercises will tone different parts of the body. Pilates and yoga are good all rounders to tone the muscles, while weight lifting, push ups, and stomach crunches can give you more defined abs and arm muscles. It usually takes a few weeks to start noticing the differences. Once you've been at it for a while, the changes become slower to progress.
It depends on the exercise. There are classes such as Body Attack that enable you to focus on burning calories and toning, however the emphasis is more on your general fitness, than on shaping. Pilates all the way for something like this. Pilates reformer classes are fantastic, and so are any other (short) classes at the gym that focus on the "core."
Yes I do think that certain exercise can shape one's figure, we only need to look at body builders and fitness models to see that. However, the right diet I believe plays just as an important role in achieving and maintaining the required physique