Rebrickable
For non-commercial use, the parts library used by Rebrickable is fairly extensive. More importantly the images have a very consistent presentation.
If you already know the part ID you can replace the use the URL below to get a direct link to the image. Just replace the X with your part ID.
https://img.rebrickable.com/img/pieces/elements/X.jpg
This won't work for parts that have alternative designs and some other exceptions.

LEGO Pick A Brick
LEGO's official Pick A Brick service has a relatively small collection of common pieces that are still in production. The images are of a consistently good quality although quite small.