(Updated for the new Blogger interface)
For a long time now, I have struggled with the fact that you can't rotate pictures in Blogger. Sometimes my pictures would show up turned to the side for no reason and nothing I have tried would work. So in the past I would either leave out that photo or crop it and try uploading it again.
1. Upload the pictures in blogger like you normally would. When you see that they will be crooked, do not add them to your post yet.
2. Go to your Picasa Web Album. The easiest way to do this is to go to https://picasaweb.google.com/home. If you are signed into your google/gmail/blogger account, then you will already be signed into Picasa Web and all of the pictures you have ever uploaded to your blog will be sitting there waiting for you.
3. Find the picture you want to rotate. Click on it. Now above the picture there is a button that says Actions. Click on it, a menu will scroll down, and then choose the option Edit in Creative Kit.
4. Rotate the picture. Save to your album. Choose the option to replace the picture.
(Sometimes the picture is already right side up at this point. Who knows why that is. If that is the case make some small change to the picture or rotate it and then rotate it back so that you can save the new right-side-up picture)
5. Now go back to your post. Click on INSERT IMAGE. On the left choose to add image from Picasa Web Album. At first the thumbnails still seemed to be sideways, but when I added the pictures to my blog they were right side up.