There are two aspects of being healthy that play off of each other: strength and flexibility. The problem with slouching and hunching is usually a lack of back or posterior chain strength. You can gain sufficient strength to maintain good posture with any amount of regular exercise--from running to weightlifting. Both slouching and hunching are the results of sitting in a chair all day and looking at things that are not ergonomically placed.
Stretching that helps is in the form of increasing your range of motion to be able to complete an exercise that you would not normally be able to do. However, it is possible to be too flexible. Essentially, if your flexibility exceeds your strength you will be prone to certain types of injury that someone who is less flexible with the same strength will not be susceptible to. For example, hyperextension related injuries.
If you approach stretching like a treatment to an ailment, things will fall into place. Not everyone is required to be able to do the splits. If your body is preventing you from doing something you want to do because it lacks the range of motion, then find stretches that increase that particular range of motion. But do it on a basic foundation of exercise. The more active you are, the more you will be able to sit and stand with good posture, and the less likely you will hyperextend your joints.