Most of the time photos are important and dear to the one taking them. It doesn't matter if the photo is blurry, shaken, crocked, eaten by a dog or whatever. That picture however is only special to the persons in it and/or the one that took it. So what could someone do if he/she/it wants to take a photo of someone and keep it interesting?
Since I'm no expert myself, I try to keep a couple of things into consideration when taking photos. Things like colors, light and shadows, perspective and patterns. Of course not everything will be present in the scene most of the time patterns. What I'm trying to do then is to think of the scene and how it would pop out, what element would make the scene show itself, because sometimes having everything in there (or giving attention to a lot of elements) may ruin the photo by being too busy.
For example if a scene has a nice interplay between light and shadow, it may be nice to tone down the colors to give more importance to the lighting. Or perhaps there is a prominent pattern going on with elements in the scene but the perspective is not exactly right. Do something; don't just stand where you were when you saw it. Go out of your way, climb something to go higher or drop down on the dirt if it's going to give you a better perspective. Try not to show things from the same angle as you saw them, simply because others would have also seen them from that angle (And this is not me being great at taking photos, it is just something that I've picked up from someone else that knows what he is talking about. When you think about it, you were walking on the same path someone else just did. So what you are seeing isn't really all that special when taken as something “new”). You see a flower that looks great? Don't just stand over it and take a photo of it. Chances are people have already seen it a million times. Drop down to its level as you may be able to get light through its leaves or petals or find a small insect there minding its own business. Go upside down, see if you can make a pattern with the grass around it…
Is there something you want to take a photo of and its angles or perspective aren't jumping out enough? Get close to it by walking if you can and zoom your lens out to its widest angle possible. You won't be doing it so that you get more stuff in the frame, as you widen your lens and you get more breathing room, you can also get closer to your subject. That would make things look exaggerated. If you want to “squash” something (perspective wise) use your lens's narrowest zoom setting and take a few steps back. Wide angles exaggerate perspective, narrow squashes it.
If something isn't contributing to the scene, don't be afraid to change it or take it out to make the rest pop out.