The upside of moving is that it forces you to make a clean sweep of the house, getting rid of items that you no longer use or need. I think it's the reason why our family tends to have only the bare minimum around our house; with so many moves, it's cheaper and easier if there's less to pack and less to load onto a moving truck.
The first place to start is to determine what to sell, either online or by hosting a garage sale, and what to give away. Sometimes, because of time or because I want to help the local community, I forego selling my things in favor of donation. It's up to you; either way, someone else is benefiting from your things and keeping it out of the landfill.
Once you've allocated the items for donation, make sure that each piece can be used, that it's in good condition and that it's been well cleaned. Next, make a list of all the items you have, then use this guide to determine where you might take those extra household items.
Clothing, Furniture, Bedding, Kitchen Supplies, and Toys
Consignment Shops: I love consignment shops, primarily because they specialize in vintage clothing, but also because they'll take some of my better-quality items, clothes that I may have worn only a few times, and offer a discount or money in exchange for selling the item. Many will only pay you once the items have been sold, while others offer you cash up front.
Thrift Shops and Non-profit Stores: These include charities such as Salvation Army, Good Will, etc. Many smaller non-profit agencies also have their storefronts with the profits going back into the community. They also work with local shelters to help ensure people receive proper clothing and supplies. Check your local directory for complete listings.
Shelters and Support Agencies: Most of our household items, in particular, clothing and bedding, is given to local shelters and other support agencies that work with individuals to help them get back on their feet. Again, check your local directory for a community organization that could use the donation.
Books, Magazines, and Office Supplies
Used bookstores: Many will take slightly-worn books, often in exchange for cash or books. If you're moving, you probably don't want more books, so look for a second-hand shop that will pay you for your beloved reads. Sometimes they'll also take magazines if they're popular reads and are not necessarily time-sensitive, i.e., news magazines.
Libraries and Literacy Groups: While your public library may not take your used books, they may ask you to donate them to a local literacy group, one that is often run through the library services. I know some of our books have found their way to some rural areas where the local library is not as well funded or equipped. Ask your librarian. They're always helpful in finding good homes for well-loved books and sometimes magazines as well.
Shelters and Other Support Services: Many shelters have in-house libraries that often act as a resource for residents and the local neighborhood. Many people are unable to access the library if they don't have a permanent address, so a shelter bookshelf is often their only resource for books and magazines. Again, call some of the area non-profit support groups and ask what their needs are and which items you'd be donating.
Schools and Daycare Centers: Your child's school may be well equipped, but unfortunately, not all schools are - some will welcome slightly-used books as long as they are appropriate for their attending students. Magazines are also sometimes welcomed, particularly in the younger grades where they are often used for crafts. This is also true of some local daycare centers.
Office Supplies: Whenever we move, there are always extra office supplies that aren't worth the cost of moving; copy paper or boxes of crayons that have been barely used. All of these items can always be used by any non-profit, with school supplies being most welcomed at schools, daycare centers, community centers, and family shelters.
Computers and Electronics
Thrift Stores and Non-profit Shops: Again, many thrift stores and non-profit shops will accept working computers and electronic equipment. Just make sure that the pieces do work and that you've erased the hard drives of any personal information.
Schools and Community Centers: Used computer equipment is often welcomed at local schools or community centers either for in-house use or for a local family or student who may benefit from the equipment. Often times if I'm not sure where to start to find someone who could use a piece of equipment, I start at my local community center. They can usually put you in touch with an organization or individual in need.
Non-profit Agencies and Shelters: Many non-profit agencies specialize in helping families get back on their feet, which may include setting up a household. A computer or stereo or television is always welcomed. There are also some non-profits that specialize in repairing broken equipment then shipping the items to areas where electronics are needed; some ship to needy families in the region while others ship overseas.