The same as the legal rights for a 19 and 20 year old. You can smoke, vote, stay out late, go to most clubs, and join the military without parental consent.
In Alabama, you can't smoke until you're nineteen.
If you're asking if, now that you're eighteen, can your parents still tell you what to do. Legally, no. Morally, yes. If you still live with them, you still have to follow their rules. They no longer have to care for you. This means you could come home one day and all of your stuff could be on the front porch. They could just tell you to leave one day, as the have no more legal responsibility for your welfare.
You cannot go into some sports bars, some clubs will require that you have a "sponsor" who is over 21 if you are between the ages of 18 and 21 to ensure that you don't drink underage. If you get caught, both you and your sponsor get kicked out. Occasionally you could be detained to wait for the arrival of the police.