Chris gave some good examples of the problems you run into, and I thought I would put my 2 cents in. The ten speed bicycle analogy is good, but can be a little confusing because there are other forces at work there. That can be mis-leading as it doesn't quite work the same with motors. The example with the hydraulic jack, and of using levers were better analogies, but it can also seem hard to relate that with gears.
Pulleys are another good example.
It may seem that, if a person can lift a piano fairly easily with the help of pulleys, then why can't we use that for energy. But, as with the lever you are trading distance for power, etc. These examples are pretty easy to see were the problems come in if you actually draw it out on a piece of paper, rather than just rolling it around in your head. Again, it is harder to see where the problem comes in with gears, but they work much in the same way as the other examples, except that it is rotary motion rather than linear motion. It is still a trade off of power versus distance.