No, they won't. You are required to provide your billing information beforehand - if you stick to the free usage tier then you will not be charged.
But if you exceed the limits they put in place, you're simply charged for what you use. There's enough Linux and Windows instance hours to run a single micro instance across a month, but if you were to run two of those instances or run a medium-sized one you would be charged for it. If you ran 1000 micro instance hours, you'd be charged for (1000-750 = 250) hours of micro instances. If you ran the medium, you'd be charged the whole lot, because that's not covered under the tier.
Whether you want to stay under it each month or not is up to you.
But they won't stop giving you the free tier until a year expires.