If this is a persistant problem, a Sears Kenmore dehumidifer costs a couple hundred and I have one. We have it on just for the summer. I know it works because I put a sopping wet baseball in front of it and it was completely dried out in two days! Wow, what a country! Don't put plants in your basement or you'll be watering them daily.
OR, you could just sponge up the condensation and water the plants with it, saving the plants and money on a dehumidifier.