If you buy bigger tires do you have to buy new wheels?

Yes, no, maybe - it's not that easy. There are several measurements to a tire; intended rim width, intended rim diameter(bead seat diameter), and profile(which refers to how thick the tire is as compared to its width). You've gotta stay with the same intended rim diameter, but you can usually fit a tire that's one size off in width w/o anything disastrous happening. Profile is the least critical of them all. As long as the rim dia is OK and the width isn't too far off you can fit a tire with a higher or lower profile(and with that a bigger or a smaller overall dia for the wheel) without any adverse effects at all on the wheel. Do note that swapping wheel sizes will affect your vehicle in several ways. Your speedo will lose its calibration, it'll affect the overall gear ratio and it can also affect vehicle stability when turning. It may also cause clearance issues with fenders and chassis components.