First and foremost, it's imperative that you try not to waterproof your basement on you're own. You'll need to contact a professional such as Champion Waterproofing to come in and get this done properly. If you do not hire an expert, you could end up dealing with a variety of issues that would otherwise not manifest. Once you've decided to go the route of hiring a contractor, the rest should be something that is common sense.
Water Damage - What people don't realize is that water doesn't need to flood a basement to be problematic. All that there needs to be is a small trickle, even a few drops here and there. In time the water accumulates and starts to rot out the walls. The rotting can cause severe damage. Not only will the damage be something visible, it can produce mold spores. If mold is found in your home, and anyone in the family breathes it, health issues will ensue. It could even cause death in some patients, which is why it's important to seal off the area.
Flooding - When dealing with the elements, flooding is possible when you have a subterranean floor. This will cause serious problems for those that aren't protected during the rainy seasons. You never know when the waters will rise and cause havoc for the home, so with that in mind make sure that you seek out professional basement waterproofing so that you don't get flooded and have to deal with the repairs that are associated with this.
Peace of Mind - No matter how old your home is, no matter how long you've lived in your house, make sure that you have peace of mind by hiring a professional to help you with the overall interior of the home. By sealing off the basement from outside options, you will rest easy when the storms arise or when mother nature sends down the worst weather you can imagine.