Doing the basics with GIMP 2.6.x, assumes no prior knowledge of any photo application, I'll do more later just did these first as they don't really need any pictures to help explain them.
Topic 1, Cropping to print/display dimensions
Your camera shoots 3:2 ratio images, you want an 10x8 (5:4 ratio) or in fact any other ratio. Open up the offending image and do the following.
1) First tool in the toolbox is the Rectangle select tool, click this or press R on your keyboard.
2) The tool option appears at the bottom half of the toolbox
3) Turn on the Check box for "Fixed: Aspect ratio"
4) In the box below type 8:10 or any other ratio you are trying to achieve. Note the portrait/landscape buttons beside this box. We typed 8:10, but we meant to type 10:8, never fear, just press the landscape button and it morphs to 10:8 without any typing, clever stuff.
5) Use your mouse to draw a box over the image you want to crop, you can resize the selection by grabbing the corners, and move it around as much as you like by grabbing the main body.
Extra Credit: Rule of thirds / Highlight
If you are having trouble visualizing how well the image will be compositionally balanced after cropping you can do the following. Under tool options on the left there is a drop down box usually defaulted to "No Guides", change this to "Rule of thirds" (you also have the option for center line and golden sections, but us photographers use the "Rule of thirds" more often than not). Your selection will now show the guides, you can still resize and move it around all you like. The guides won't show on the final crop, they are just a visual guide.
If you are trying to crop out distracting elements in the photo you may still be having a hard time visualizing the crop with those distracting elements still on screen. Under tool options click the "Highlight" check box. Now anything outside your selection will be temporarily darkened so you can focus on the area you want to crop. You can still resize and move the crop area as much as you want. None of the image is actually darkened this is just a visual guide.
6) When you are happy with the crop, use the drop down menus at the top of the image window, choose Image >> Crop to Selection. Everything outside your selection is discarded and the canvas is resized around your crop. If you change your mind you can press Ctrl+Z or Edit >> Undo and re-adjust your crop. You should always keep the original image intact in case you change your mind on how to crop it again later, so at this point go to File >> Save As and save with a different filename (i usually add _GIMP_edit to the end of the original file name).
Topic 2, 100% Crops
You have picked up a bad case of pixel peeping syndrome. At the moment you have not realized that you can't see the picture for the pixels, or the wood for the trees, so you are hell bent on getting a 100% crop of 500x500 pixels to share with you co-infected 
1) First tool in the toolbox is the Rectangle select tool, click this or press R on your keyboard.
2) The tool option appears at the bottom half of the toolbox
3) Turn on the Check box for "Fixed: Size"
4) In the box below type 500x500 or any other size you are trying to achieve. Note an alternative longer way of doing this is, Fixed: Aspect Ratio, 1:1, and set the two size boxes to 500px.
5) Use your mouse to place the box over the image you want to crop, you can't resize the selection as you have fixed its size, but you can move it around as much as you like.
6) When you have the section you want, either press Ctrl+C or go to Edit >> Copy.
7) To make this selection a completely separate file press Shift+Ctrl+V or go to Edit >> Paste as >> New Image
8 ) You can now save this crop probably as a quality 100 jpeg for full quality, or quality 80 if you are trying to keep the size down. Even going from 100 to 95 can save a lot of space.
Tips!
If you intend to come back to these files and edit them some more you are best saving them as a .xcf file (gimps internal loss-less format). If you find the .xcf takes up a lot of space when you save it give it the double file extension of .xcf.bz2, this will save it as .xcf but also compress it with bzip2 which should reduce it to about 10% the disk space, but still full 100% quality.
GIMP is smart enough to know to bunzip2 .bz2 file then open the .xcf contained inside, however Windows may not be so clever so if you add the .bz2 you may have to open the file directly with GIMP, as windows knows gimp handles .xcf files, but does not know that it also handles .xcf.bz2 files as windows was not built with double file types in mind. Your mileage will vary with other operating systems.
Good luck, feel free to add your own cropping tips to this thread. I'll do levels/colour/white balance/resize and plugin installs/black and white conversions/requests at some stage in the near future in a separate thread, and eventually a thread that links them all together.
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