I took 9 AP classes in high school overall, all fives but two, and all I got into was NYU
Universities like Princeton and Stanford essentially expect you be taking the most difficult classes in your high school. This, however, is not the reason to take them. The reason to take them is that you will learn so much more, and probably enjoy them much more too.
While you may not realize it at the moment, high school is incredibly easy! It becomes easier when you are taking classes that inspire you intellectually. A big advantage of AP/Advanced/Honors classes is that more of your classmates actually care about what they are learning, and this is a tremendous help in making school interesting instead of soul-sucking.
If you are worrying your grades might suffer from taking advanced classes: don't. It might be a bit more work than you are used to at first, but it is no where near the limit of what you are capable of.
Now, taking advanced classes is only the start of what you should be doing. You should be going above and beyond your school work. Once you are settled in, you should be reading on your own. The trick is to not be doing trivial things. Ask yourself: "A year from now, will I care that I did this?" If the answer is no (such as it would be for watching a TV program, or making a post to a message board

), then it's not worth it.
Most importantly, though, is to make the most of your time in high school. By that, I don't mean drinking with your friends every night. I mean try to trust me when I say that at this point in your life, you have more freedom to explore things than you ever will. Think of your homework assignments and those pesky seven hours of class as a required minumum. Above that, you have so much time to let yourself wander. Use it.