Can I trade in my current iPhone when I purchase a new one through Apple's iPhone Upgrade Program?

This depends on the model iPhone you wish to trade in. Models more than a few years old will not likely be accepted for trade-ins. You can check your eligibility through the Apple Store app or website. The value of your trade-in will depend on the model and condition. If you sign up at an Apple Store your trade-in value will be applied to your purchase. If you enroll online you will receive a gift card.