Brian from Cornwall, Ontario just bought a house and when it rains heavily, it flows in the basement. Someone recommended that he dig a trench inside the basement to drain the water away.
First of all, see if simply landscaping sloping away from the house, and rain gutters and downspouts away from the house won't solve the problem without any inside work.
If you can't stop it from the outside, you can let it in and control it. Basically either you dig up the perimeter of the slab and put a drain all the way around at the level of the footings, or you put a vinyl channel, sealed to the floor that will catch any water coming in and direct it to a drain or a sump pump pit. This is most commonly down with cinder block walls because there is so much mortar that it is hardly worth trying to seal cracks, and simply drilling into the hollow part of the blocks will get to any accumulated water.
For a full discussion on basement leaking options, see Basement Perimeter Drainage and Leaking Foundations.