Being flexible helps prevent injury when your body gets put in awkward positions, which can happen pretty frequently in many sports and daily activities. Being flexible is also more and more useful to you as you get older, when your balance is not as good and falling often leads indirectly to death(broken hip/leg/arm leads to hospital stay/exposure during which your compromised immune system catches the ever-present pneumonia in those environs and you croak). You also tend to be a lot stiffer, increasing chances you will pull muscles or, when falling, be unable to correct yourself in time -- again leading to situations that can take you from perfect health to death within a matter of days.
It's wise to maintain flexibility, and it's far easier to work on when you are younger than when you are older. If you want to think ahead, take care of yourself now while it's still no big deal. You can get all the flexibility work you need in 10 or 15 minutes on the floor in front of the t.v. set every other day, or you can do most of it in bed before you fall asleep. It can actually relax you and release endorphins, so it's not a bad sleeping pill or way to unwind from a day's work.