Does having much knowledge in other branches help one's research in mathematics in one's own field? I am wondering if having much knowledge in other (seemingly not directly related) branches of mathematics is helpful to a mathematician in his own research. Say there are two algebraic topologists A and B. A also has some knowledge in PDE (say he knows the basics of graduate level PDE well and can even teach a graduate course on PDE) and B does not even know the very basics of ODE. Does this make any difference in their ability in doing research in algebraic topology?

I know that some fields are somehow related; for example, it will help a group theorist if he knows algebraic topology or number theory; but how about other fields that are not apparently related, such as the example that I have quoted?
The answer is yes. It helps. Mathematics is very broad. In the various major branches, such as Analysis, Algebra, etc. different insights are needed to really understand what is going on and what is important. In addition to the all-important insights, different proof techniques are common. 

When you are doing real research in mathematics you are engaged in a very narrow study. But having a wide variety of ways to attack a problem, even if they might be suggested by ideas from another subfield, will give you an advantage. 

Both breadth and depth are needed. Depth is usually what is most valued, but the breadth of knowledge helps you get there. So, don't completely neglect other mathematical subfields than the one you are most interested in. You don't need to be equally skilled in all of them, but being able to grasp the essential insights is a plus.