A free image hosting service that won't re-size or lower the quality of my images?

Google’s Picasaweb

https://picasaweb.google.com/home

As well as allowing full-scale uploads, it will do on-the-fly resizing for you. For example, I uploaded this photo once, but I can get different sizes by simply changing the URL (note the s800, s400 and s200).

https://lh4.googleusercontent.com/-dBFXcGG1O6c/SWs9EQoj-UI/AAAAAAAABpQ/C6KjD7uwspY/s800/P1100152.jpg

https://lh4.googleusercontent.com/-dBFXcGG1O6c/SWs9EQoj-UI/AAAAAAAABpQ/C6KjD7uwspY/s400/P1100152.jpg

https://lh4.googleusercontent.com/-dBFXcGG1O6c/SWs9EQoj-UI/AAAAAAAABpQ/C6KjD7uwspY/s200/P1100152.jpg

I really like the Picasa desktop application, too, for organizing pictures. It just works. If you move items among folders in Picasa, it actually moves them on your hard drive. Conversely, if you move things around on your drive, Picasa automatically and instantly reflects the changes.

If you’re doing web design, do you also have some web hosting that you use?

You can easily upload your files there via FTP and then you have complete control over them. Hosting the images separately from the rest of the site can cause some issues.

I understand you’ve probably considered it, but wanted to mention it just in case. If you need help with the FTP part, most hosts offer some sort of guide, or even web based tools to use.