Does radiation ever cure cancers, or does it just shrink them?

It can cure cancer. Radiation is used cureatively and palliatively which means its use is to cure or relieve symptoms. Radiation can shrink tumors and hopefully shrink them all the way to dead cancer cells when cure is the intent.
Depends on type. Radiation is used for curative intent of anal cancer, cervix cancer, skin cancer, prostate cancer to name a few. Additionally in many other sites it is a vital part of the treatment process to keep the disease from returning called local therapy or local control such as in breast, etc. In breast cancer, surgery is utilized as well.
Yes, but... Radiation therapy, and new innovative types of radiotherapy such as stereotactic body radiotherapy (sbrt) have been proven to be beneficial in early and late stage lung cancer. However, the standard of care for treatment for cure of early stage (i and ii) lung cancer in the physically fit patient is surgery. See www. Cancer. Gov.
Yes. Fortunately radiation has been used with good success in terms of curing people from the cancer. Some examples are treating cancer of larynx, or skin with traditional fractionated radiation. We have used radiosurgery with excellent success in treating early stage lung cancer.
Both/Neither. Prostate cancer is a classic of where it cures without shrinking; but aiming at bulky lymphoma may shrink without curing. Many times we treat the invisible (breast after lumpectomy) and it cures and controls, and other times we can treat very large problems or resistant types and it rarely shrinks or cures. "just shrinking" to releive suffering is a good thing.