Of course you can't touch your eyeball with your finger. It is really bad to our eyes. As we all know, eyes are the most delicate and tenderest part of human body, so we should take good care care of it and doesn't harm it. Our finger is full of bacterium and if you touch your eyeball, it is easy to get infected. Then you may get many kinds of eye diseases. Eyes are the window of our heart, so we should treasure it.
Almostly, people do not touch their eyeball directly. It's OK for you touch it accidentally if your hands are clean. While, unclean hands can have a lot of bacteria, which may cause eye infection. If you have any uncomfortable feeling for touching your eyeball, ask your doctor for professional suggestion.
Well, of course, it is ok for you to touch your eyeball. For example, when you wear contact lens, you have to touch your eyeball to put on them, and then touch them again to take them off. And that can be fine. But you need to keep your fingers clean, or it will just make your eyes infected. And then, some eye problems may occur because of the dirty fingers. Anyway, just be careful too, when you touch your eyeball.