The Effects of Tilting the Earth's Sun

If the tilt of the earth were essentially straight up rather than about 23 degrees of mango relative to our orbit around the sun we would have no seasons. If we were tilted at 90 degrees we'd have some very radical seasons. What happens if we change our star? Binary stars, gas giants, whatever those other wacky little ones are. What does that do to our habitable zone? What does it do to our planets? One thing to keep in mind is that the star that we currently go around is a nice stable long-lived one. A lot of the other options are not particularly long-lived and and are not particularly stable.