Is it true that once you're in your 20's, your vision doesn't get any worse? (your eye sight stabilizes)

Mostly true: As you grow through the teens, the power of eyeglasses if you need them will progressively increase although at a slower rate. For most this process stops in the mid 20s and stabilizes for many years until other issues of middle age sight start to happen. This is why most LASIK surgeons want you to wait until you are 23 or so prior to doing the surgery.