There are a variety of things to do with old books that you no longer want, depending on their condition and content. You might choose to donate old books, sell them to a bookstore for cash or trade, pass them on to friends, or simply throw them out if they are in poor shape. There is no reason to allow old books to accumulate when others might be able to find a good use for them.
When you are deciding what to do with old books, asses their condition first. If the book is a hardcover and the dust jacket is still in good shape, it might be salable. If it is a ratty old paperback with torn cover and pages, it sounds like a good candidate for donation or recycling. Check to make sure that the book has all of its pages, the cover is not coming off, and the pages or covers are not stained. If the old books are in good condition, selling them to a used bookstore might net a small amount of cash. They could also be donated to charity, if you felt so inclined, along with books in less perfect condition.
When selling old books to a bookstore, be aware that book buyers are often looking for something in particular. It is important to be aware of the content of old books if you are bringing them to a bookstore, because some topics are of more general interest than others. Fiction is usually a safe bet, for example: travel guides are not. Book buyers know what sells in the store and what does not, and they may decline some of the old books as a result. Most used bookstores also offer a higher rate of trade than cash, and you may want to consider accepting trade and swapping your unwanted old books for a fresh set.
If donating old books to charity, avoid donating books that are in truly poor condition. If you think the book should be recycled, toss it, rather than forcing the charity to reach the same decision and clogging up their recycling bins. If a book is stained, warped due to water damage, or missing a cover, a charity cannot sell it or give it out. Most charities also prefer that you enter the charity with your donation, rather than leaving it on the step to be rifled through and potentially damaged. Charities can also provide you with a receipt for tax write off purposes, if you need one.
You may also want to consider exchanging books with friends. You could simply have a shelf of old books that you don't want by the door, and encourage your friends to take books that looked interesting. If your entire social network followed this practice, a constantly circulating library of old books could be formed. You could also have a book swap party, where everyone brings a box of old books to a central location for the others to look through. After the book swap, box up the remainder of the books and donate them to charity.