Not having red eyes in photographs does not mean cancer. Most of the time it just means you took a photo the correct way to avoid red eye. The time to be concerned is when a photograph shows a white reflection under red eye conditions instead of red. Retinoblastoma is a type of eye cancer where a tumor forms in front of the retina. Because red eye is illumination of the retina of the eye, in a photograph that normally shows red eye retinoblastoma will sometimes show up as a white glow because the white tumor is being illuminated instead of a healthy retina. It is also worth noting that most of the time this type of cancer occurs in only one eye so images will show one red eye and one white eye. There are other symptoms as well and detailed information on those can be found at Retinoblastoma.net.
Also, to dog owners now concerned about their dog's photos where the eyes glow white, a white glow is normal for many animals. This is part of the "green eye" phenomenon and is caused by a different eye structure than humans.