Why are some of the images on my blog and the blogs I try to go to suddenly not showing up. I just get a white box with a red X.

Where the images linked to another site?
The site has more than likely removed the image or put a block on it to prevent people using their bandwidth.

No, they are images directly from my picture files or other bloggers pictures and it is completely random. One of my pictures will show up and one won't from the same file.