Make sure to focus correctly, especially when it's up close (the photo above is a good example of me not focusing the camera very well, but the photo below a good example of good focus).
Include the scene around the subject (but beware of poles or objects looking like they're going through the subject like the one coming out of her head here). This works well with a great depth of field if the background is important to the photo.
Wrinkles are interesting and window light is your friend. Details in people's faces add interest and putting someone next to a window gets natural lighting you can manipulate by moving the person around or using different angles based on where the window is.
Don't accidentally be in the photo. In the first photo here, you can see me taking the photo in the reflection, but you can't in the second one, plus the composition is better.
Show personality. Photos are more interesting when they show you something about a person. Don't be afraid to be silly or funny. Photos don't need to be serious if you don't want them to be.
Everyone looks good during the golden hour (the hour or two before the sun goes down or after the sun comes up).