I've never been very flexible, but I've found that stretching helps me maintain the flexibility I do have and also helps me to decrease muscle soreness after harder workouts. One of the physical therapists I worked with a few years ago started a personal yoga routine with amazing results in his flexibility and he reported he didn't realize how trapped he was with his lack of flexibility at the beginning until his body could actually move more following the program.
Not only is stretching great for increasing your flexibility and range of motion, but it can be a great stress relief. I've found on nights I can't quiet my mind enough to fall asleep, it is helpful if I do some stretching and deep breathing to help me relax. It helps me turn off my mind.
Stretching can also increase blood flow to your muscles, which can help decrease muscle soreness and promote muscle repair. You might find your posture improved, low back pain decreased, and overall feeling more "free" in your ability to move!
Do you enjoy stretching, or tend to avoid it?