A friend asked me recently what the difference is between the knife and scissors tools. You'll notice in the image above that the knife tends to cut on a squiggly path. It also creates closed shapes, which isn't always what you want when modifying a shape.
Personally, I prefer the scissors tool (C). You can cut anywhere on the path to get exactly the line that you want. For closed shapes, you get more control by using the pathfinder palette with overlapping shapes.
Hope you found this tip useful! If you have an Illustrator question feel free to ask. Or, if you have a suggestion for a tip, feel free to let me know.