Initializing arrays, potentially unforseen consequences?

I've recently observed that by initializing an array, the garbage values are all replaced by null terminators. This would appear to be inconsequential, but in a large program I don't think it would be preferable to spend resources on cleaning out an array. Now to be clear, I don't program large programs, that's why I'm asking, I'm just a beginner. However, when used properly, it would stand to reason that garbage values would be perfectly fine as long as there is always an explicitly placed terminator.

So then, should I take it as bible to always initialize my arrays, or should I consider whether I can get away with leaving the garbage values untouched?