I maintain a photo life list. When I come upon a new bird, the first priority for me is to get an image. These vary in quality depending on the circumstances i.e.weather, lighting, patience of the bird (and the photographer), the background, etc. I will often take an insurance shot at distance just to be sure I have at least one image. Sometimes that is the only one I manage to get.
Once that is out of the way I try for two types of shots. 1) close up of the bird showing detail and colour 2) environment and setting type pictures where the bird makes up a smaller proportion of the frame.
Once I have a good quality record shot, I look for upgrades to the shot. If I have a good quality record shot, I discard all poorly focused, badly exposed, poorly composed, photos with distracting elements etc. As another poster mentioned a catch light is essential as is having the eye in focus. Also as he mentioned, leaving space for the bird to move into or to look to is good. It the bird has long legs, don't cut off the legs even though they are hidden in the grass or in the water. If the eye isn't in focus I discard the image.
Perhaps the most important aspect is to visualize the image before you take the picture. Exercise patience before pressing the shutter. Wait for the head to be turned the right way, see if there are distracting elements in the picture (cropping after the fact can sometimes fix this), try for an interesting background etc. If the lighting is too difficult or the setting is not interesting just pass on the photo and move on. This is easier to do on more common birds in a home patch. A little more difficult with a rare bird or when traveling.
I've attached a couple of examples. There are more in my 2014 add and upgrade list, generally the upgrades will be more "creative" than the adds for the reasons mentioned above.
Paul
2014 adds and upgrades to photo life list
http://paultavares.smugmug.com/Wildlife/Birds/AU14/i-vLwsKSB