When I want to get rid of something, the first place I consider is eBay -- for lightweight, brand-name items in near-fine condition.
The second place is Craig's List, for large items that I know will sell quickly (TVs, computers, dining room tables, sofas, lawnmowers, etc.).
The third place is a local consignment shop, Classic Consignment, for furniture, clothing items, and small household items in good shape and fairly trendy. The advantage to taking something to consignment is that you don't have to "babysit" the item or worry people coming to your house.
Items in decent-but-not-wonderful shape, or in good shape but out of fashion, go to Goodwill or another charity.
Recently I came across a fifth option for "giveaways" that are just too odd, or unwieldy, to take to Goodwill: The Freecycle Network -- specifically, the local Seattle chapter. What do I mean by "odd"? Check out Freecycle.
If someone likes something you have listed, they email you. You wait a few hours, sort through the emails, pick a likely recipient (someone who lives near you, or who wants to pick the item up at a time convenient to you), and email (or call) them to set up a time for pickup. Or list a want and see if someone responds.