http://www.waterproof.com/ The Squidgee Dry Channel System. This would be one option for you, depending on how finished out your basement is. This won't stop water from entering, but it will channel it to your drains. Without a sump or tile system, stopping water from coming in in the manner you describe is not very feasible. That water MUST go somewhere, and preventing it in one place will only make it go to the next weakest point.
As your basement has no sump, you're not likely to have a drain tile system at all, so there's one other important thing to be done to help prevent further problem, or at least keep it to a minimum; proper drainage around the home.
When conditions outside get better, check to be sure you have good drainage all the way around the home. Use downspout extensions where needed to minimize the amount of water entering the soil near your house. Check for any low areas next to outer walls which might hold water, and fill them with topsoil.
Planter beds next to the walls are often a problem; they can often look like they drain well, but the soil level below gravel or decorative covering may drain towards the house, rather than away, so be sure that any decorative coverings aren't being deceptive in thier looks.
Your first, and least expensive, line of defense against water entering your basement is maintaining good grade and drainage around your home, especially within the first 10' to 15' next to the structure.