Just because you don't see any water doesn't mean that the water is gone. The water is sitting either in your wall or just behind your wall which will lead to major health problems if not removed. Think about that cooler in your garage that you forgot to empty a week or two ago. Recall the growth? The smell? Consider that cooler year round behind the walls of you or your kid's bedroom. It's neither pleasant nor health.
That's is similar to what is happening this very moment in thousands of homes throughout the Northeast. If you are currently (or have ever for that matter) witnessed even a little bit of water coming into your basement, you can rest assured that there is a lot more water sitting behind your wall. This is because it takes significant pressure to push water into your basement the first time. But once water breaks through, the avenue only widens with time.
If you do not seal your basement then mold will start to grow. You will likely smell it before you see it. Have you ever been in a basement that was not leaking and smelled a damp musty smell? That's because the basement walls have been compromised and water has caused mold to grow inside of the walls. Mold can and likely will lead to health problems if not taken care of. Consider the fact that home furnaces are commonly placed in basements, sucking in the ambient air down there, and systematically spreading mold spores into each and every room of the house.
The bottom line for the safety of you and your family is this. If you smell musty air in your basement, have your home checked for water, mold, and mildew. It really is that simple.