Sometimes I try to pour a cup of coffee while the coffee maker is still brewing. In the past when I've done this, the machine will stop brewing while I poured, but now it keeps brewing and drips onto the hot plate.
If you pull out the filter holder and look at the bottom you will see a rubber ball on a paddle stick which is the stopper to prevent the coffee from leaking when you pull the carafe away.
I've had to clean mine a few times as the grains of coffee can sometimes prevent the sealing of the opening. If the rubber is hard it maybe time to replace the part.
Good tips, Dan. As said above, there is a ball and spring mechanism that is part of the filter basket. If you still experience the problem after you clean it, they do offer new filter baskets online that come with the ball and spring mechanism. Here is a link to the troubleshooting page that has a guide which details how to replace the filter basket and also has links to websites that offer the filter basket replacement part.
This could also occur due to overflowing. If too much water was poured into the reservoir, the filter basket could overflow if the carafe is removed for too long.