Since I wasn't satisfied with the way I did the CLAMP style eyes, I felt that I had to do another tutorial. Since I already covered CLAMP's eye shape, I'll just go over anime eyes in general. I will introduce to you a way to draw eyes that might make you slap yourself. >.<
"Flat" Eye
Here, we begin with the inside of the top eyelid. This will be based on the shape of the face, depending on the effect you want.

Next, we extend the top eyelid with a slightly curved line. The end of this line should tend to go a bit more downward than the first line, giving the effect of a "realistic" eyelid.

Third, we draw a line for where the pupil will "sit." I say this because it's about the width the pupil will be later on. Notice how it's slightly to the side of the first line.

Fourth, we draw a line slanting upwards. The key to pay attention to is to not allow it to extend beyond the upper eyelid. (The bottom eyelid should be shorter than the top and within its borders. Refer to the vertical lines.)

We add dots to get an idea of the eyebrow shape we want. This works better than drawing lines for me, since it is cleaner. If you're decent at making eyebrows, just skip this part.

Lastly, finish the eyebrow and add width by a second line slightly above the first line. It should kinda hug the shape of the first line.