The most important thing to remember when drawing eyes, even in a 2D art style, is that eyes are spherical, and that the eyeball exists underneath the skin even when we can't see all of it.
It's good to think of the eyeball as a 3D shape, and think of the eyelids and the skin around the eye as a window that's placed in front of the object.
Though it's unnecessary to draw the eye as a perfect circle every time, using a rough circle to place your eyes before you add the eyelids will help you:
Place your eyes symmetrically,
Always ensure your characters' eyes look focused in the proper direction,
Shade your eyes more realistically and convincingly,
Understand depth when drawing the eyes at unusual angles or from the side.
If you'd like to draw a character with puffiness under their eyes, or defined upper eyelids, drawing this underlying circle also lets you convincingly place lines to represent those features without sacrificing stylization. You can also use the placement of this upper eyelid to proportion the eyebrows.
Once you understand the underlying shapes of the eye, even drawing really simple cartoonish eyes becomes quick and easy, simplified into just a few strokes!