Maybe you are hyperextending the leg.
In other words, you may be pulling on the IK handle beyond the leg's maximum extension. Try this; grab the IK handle at the ankle then only move it far enough to straighten the leg but not any further that that. Also, make sure the IK leg motion is not moving faster than the rest of the body. The snap could be caused by the leg hyperextending followed by the rest of body catching up to it. If you rigged your model correctly, when you move its body down from the root joint (usually the pelvis) the legs will bend. This means that the bend in the legs can be caused by moving the IK handles on the model's ankle and also from the movement of the rest of the body. Basically, this means that the body movement and the leg IKs can either work together or they can work against eachother..
Remember that the IK handle moves in a straight line so, if you are trying to get the ankle to move in an arc, you will have to add keyframes every so often to simulate the arc. Don't try to get too much motion out of a single keyframe. It's hard to explain without showing you drawing but I don't have any right now..