Cropping photos of people can be tricky. There are so many parts of the human body you can cut off! This photography cropping illustration from Digital Camera World shows you the best — and worst — areas to crop a subject so you can avoid creating awkward people photos.
The green lines are the "good" places to crop and the red lines are the ones to avoid. So, for example, if you're not cropping above the elbow, you should show the elbow, wrist and hands. Here's the cheat sheet, which might come in handy, whether you're editing the photo on your computer or stepping in closer to get a more interesting photo (click to expand, right-click to save):
The guide essentially follows the rule of "don't crop off at the joints". A few commenters on Digital Photography World, however, say the green crop line at the knees breaks that rule, but the illustration might be suggesting to crop just above the knees. You can play around with that crop area to see what looks best to you; as long as the person doesn't look amputated, you've avoided the biggest issue with cropping people photos!
Digital Camera World has several other photography cheat sheets that might be of interest to you too.
Free portrait photography cropping guide [Digital Camera World]