Can science prove a theory, or can it only disprove a theory?

Technically, what science deals with are hypotheses. A theory is a hypothesis which has been well supported by experiments. However, hypotheses, and even theories, are most always considered to be tentative. That is, it is always allowed that some valid experiment could show that the hypotheses is incorrect, either wholly or in part (referred to as falsifiability), so that it must be rejected or modified. So in science, absolute proof is usually impossible. Essentially it would require proving a universal negative: this hypothesis does not fail under any circumstance. And as they say, to prove a universal negative requires universal knowledge. A hypothesis which is not "falsifiable" is not generally considered to be scientific. That's not the same as being untrue; there might be any number of truths which are all the same beyond the reach of science.

It's been said that science can't prove a theory. That's true in a sense, but science has proved a number of things in the history of mankind.

The round earth started as a conjecture, then a hypothesis, then a theory (hotly condemned by religious folk along the way).

Orbital mechanics and gravity followed much the same route.

As did germ theory of medicine.

Ditto the theory of light.

The above are all now indisputable fact.

Evolution theory is going through the same trials today, but there will come a day when the religious folk have to admit the truth about the origins of life on Earth and move on to attacking some newer scientific theory.

I beg to differ, HungryGuy.

Science is nothing more or less than a method of enquiry based on hypothesis testing facilitated by data collection. It is distinct from - though intimately connected to - logic and rationality. Notably, the concept of falsifiability is key to this tradition - hypotheses must be stated in such a way that they can be disproven with but one antagonistic observation.

The round earth was proven not using scientific methodology but by dint of simple observation (from space). Saying that that is science is tantamount to saying that we can scientifically prove the length of a table by laying a ruler against it. Data collection is part of science, but data collection alone is not science.

Orbital mechanics, gravitational theory, light theory, and medical germ theory have not been proven. They are just accepted as true insofar as we are aware today. Oh, yes, there are mathematical proofs for the first three sets of theories, but mathematical proof is a completely different beast than scientific proof.

Science doesn't prove a thing, but that doesn't mean science is useless! What science does is pare away less plausible explanations for any given phenomenon, thereby hopefully leading us closer and closer to the truth about the phenomenon. Of course, it can fail to significantly improve our understanding of a topic or even lead us temporarily away from the truth. However, when applied correctly and with a bit of luck, it can vastly increase human comprehension of the natural world.

jalex137's excellent answer at the top of the page is pretty much all there is to say about this topic, really.

It is my understanding that the word "theory" is adopted today by scientists instead of "law" not so much because it will be proven incorrect, but because it (a theory) may later be subsumed as a smaller component into a larger framework (theory). And on and on it goes. Think of it this way. Newton boldy called his discoveries "law" (of gravitation) but his discoveries were subsumed and even corrected by Einsteins "theory" of relativity. And it was called "theory" as a convention of the modern times. A theory corrected a law.

Only religion or politics can prove a theory (heaven and hell, democracy is best...).
Science can only test for failures of theory, and try to think of more tests.