It is acceptable to give a secondhand book as a gift when a new copy is unavailable or when something is special about the secondhand book. It is also fine when the giver knows that the recipient does not mind receiving a secondhand gift.
A secondhand copy of an out-of-print book can make an excellent gift. Book reviewers often sell review copies to used bookstores, so snagging one of these before its official publication date means the giftee gets to read it before everyone else.
Books that are antiques, vintage, first edition collectors' items and autographed copies are valuable enough that people do not even think of them as secondhand. A book that belonged to someone special such as a grandparent may be cherished for its sentimental value.
Some people even prefer secondhand gifts. They are part of the "green" trend, a movement dedicated to leaving a smaller footprint on the environment in part by reusing items rather than buying newly manufactured ones. Being open about exchanging used gifts before the fact means that both parties can save money by giving secondhand items.