Well, the simple answer to "how much can you crop an image" is as much as you're comfortable. A couple of the big questions would be "what is the use of the shot" and "how was it shot"? If you're using a DSLR, have a 2 GB memory card and can shoot a million images, the answer would probably be not much. The camera would have to be set to the absolute maximum compression and lowest resolution. Those images are meant to be used on your Facebook page or somewhere else on line. You can probably get a reasonable 4 x 6 print out of it, but not much more. If your camera is a new Nikon D800 and you shoot in Raw, you can probably print a billboard sized image that would look pretty good. Today's question came from a friend (okay, a relative) new to photography. He/she wasn't sure if she/he could print images the size I do with her camera, a Nikon D3200. Again, well... that's a 24.2 Mega Pixel camera. It's not quite a D800, but that's still a lot of pixels. I print (have printed) images up to 24" x 36". That's not often, but enough that I can offer it. The "friend" said he/she had an 11" x 14" made from one image and it looked like crap. I asked about the number of shots would typically be taken on a day of heavy shooting (undoubtedly the grandkids). The answer was "oh, a lot. Maybe as many as 60 or 70". If you're a shooter, that a really light shooting day (hour). The camera had been set to get the maximum number of images. We reset it to get the best possible JPEG images. There's no image improvement being done on any of this person's shots, so there's no point to shooting RAW. (Maybe next year.) Today's image is an example of about the maximum cropping I do. Hit the "Read More" to find my thoughts on cropping.
Other than for format, my thing is to crop in the camera. Take a look at today's image. Look side to side. It's the full width of what came out of the camera. There's a little bit of Perspective Control tossed in (and a little more in the final image), but other than that it's all there. The cropping is top and bottom to get the aspect ratio that works with the image. After the crop there was still a little triangle of sky to the left of the tree truck. A tiny amount of cloning using the Clone Stamp Tool (S) made short work of that distraction.
My reasoning for cropping in the camera is that I want to see what I'm going to have when I'm shooting. I've always done it and the only caveat I can give is that I will crop in both directions if the lens isn't quite long enough. Then it's typically only a small ring around the subject that's removed. If I can't "almost" fill the frame it isn't only to make a good shot anyway, so why bother. Rick Sammon is always running around saying "the name of the game is fill the frame". He's pretty much right on that one.