If my blood type is O positive, what are the possiblt blood types of my parents?

If both of your parents are type O (which only means they lack A and B antigens) then your only possible blood type would be O.  However, you can be type O and have parents that are type A, type B, or type O.
A person will carry two copies of that gene, one from each parent.  If they have an A and an O they will be type A, same as if they had two A's.  So your parents could have had the genes OO, AO, or BO but not type AB otherwise you would have got an A or B from that parent.
The positive part deals with the RH factor.  The positive just means that you have at least one parent that was RH positive.
As a blood type O positive is pretty common.  O positive blood can be transfused to anybody that is A positive, B positive, AB positive or O positive.