You have a header image and want the very left and/or right one-pixel line in order to be able to nicely repeat it.

First find out the width/height of the banner (in the example case its 192x800 pixel) - then just use crop (works with gif/jpg etc too) 

This is probably the most usefull function - and pretty easy to use.

While supporting a big portal (the teendays event), I found out that most thumbnails created (they were only max 100x100pixels) where a few kilobytes big... too big in my opinion. I found out that the problem is the profile stored in the images, after removing the profile with the option "+profile *" the files shrank to about 1k - 2-4k smaller than before without quality loss!!!
 

If the thumbnails are poor quality you might want to play around with " -quality 70" (change number)

Videos are getting bigger and bigger nowadays. If you want a preview image of your avis imagemagick is a great help there too.

Remember: you can always use resize too. the [0] is the first frame of the video... you can increase the number if you want an image form in between