Something I have been trying to do in my own photos is to try cropping them to make them a bit more interesting. I do like cropping because I think it engages the viewer in a game of guessing what's happening outside of the photo. It can also be used to hide unwanted aspects in a photo. Take this terrible photo for example. It was taken by a friend about a year ago. The raw photo is terrible (no offence to my friend). I have marks on my face from my glasses, my hair is fuzzy, I'm not smiling and my face somehow looks saggy.
I increased the contrast, brightness and saturation because this is how I like my photos to look. I also erased the background and then cropped the photo in 2 different ways. First I focused on the top half of the face. You can see this picture on my profile. I thought this worked quite well because it provides a hint of what I look like but without giving the game away completely. Once I got the cropped version I noticed how stunning the eyes looked and decided to try cropping further in order to focus on this.
I have another example of good use of cropping here.