How long are prescribed drugs legal to take?

The prescription will specify the time period; if not, it's "until they run out" (note that they should be discarded once they reach their expiration date, but this is for health rather than legal reasons).

If you keep getting prescriptions, you can take them essentially as long as you live. There's no hard and fast time limit like "you can only take Vicodin for three years, and then it becomes illegal." The fact that a physician must prescribe them for you is considered a sufficient restriction against abuse.

Note that a physician may not be able to supply you with an open-ended prescription (i.e. "refill as needed"), but you don't really need to worry about that; it's the physicians job to limit the number of refills.

You take the prescribed drugs as Directed by your physician with any advice from your pharmacist. All prescription medications should be appropriately discarded a year after being filled unless otherwise stated. But legally if you possess a validly filled prescription you can legally take it.