Letting them ripen on the vine, and picking them as they get ripe is one reason people like to grow tomato's at home. Deep red tomato's that just came off the vine are the best there is.
Pick them prior to ripening only when it is absolutely necessary. Like at the end of the season when frost is near. Picking them earlier actually saves little time. It will take just as long to ripen whether they are on or off the vine, but I believe they get tastier if left on the vine.
At the end of the growing season, when a danger of frost is near, is about the only time I pick green ones. Leaving them on the window sill is one option. Keeping them in a brown paper bag until ripe is another. And making green tomato relish is another.
If you get overrun with red tomato's, You can make homemade salsa, sauce, or ketchup, or crush them and throw them in soup. I have even frozen ripe tomato's whole and used them in soups during the winter.