The cost of labor is usually the most expensive component of kitchen remodeling, so any work you can do yourself will result in big savings. Of course, you need to realistically rate your diy skills before getting into a job like this. If the only time you've ever held a hammer was to hang a picture, then you probably don't want to take on a complete kitchen remodel yourself. But you still might be able to save some money by doing all or part of the demolition of the old kitchen. Safety is the main consideration here. Get your contractor's opinion on whether or not a novice would be able to handle what's involved in the demoliton portion of your renovation, and be sure to get an idea of proper safety procedures by reading a book or two and watching some do it yourself TV shows.
On the other hand, if you've had some diy experience, even if it's only building a deck or a bookcase, you may be able to do part of even all of a small kitchen renovation or simple remodel. By simple, I mean something that doesn't require moving any utilities. If your plans require relocating any pipes or wires, best to leave the job to a licensed contractor. You definitely do want to make sure that the job falls within your skill level before starting, though. If you have to call in a pro halfway through because you're stuck, you'll probably wind up paying them as much as you would have to do the whole job right from the start.