Let me start by saying I've probably won three times as much on Twitter as all the other ways. And contrary to popular perception, you do not have to participate on Twitter via your cell phone...it can all be done online.
First, follow your favorite brands on Twitter. They frequently hold Twitter only contests for free full size products, promotional items, etc. Because Twitter has significantly lower usage than Facebook, you have much better odds!!
Second, follow your local venues. Tickets are given away via Twitter on a regular basis. They may be last minute for that same day's show...but if you're an empty nester like me...it's easy to get up and go!!
Third, follow your friends! They may be following brands, venues, etc. that you may be interested in but they've already done the work of finding them!
Fourth, follow your favorite blogs. They will post links to their own giveaways, Twitter contests, and giveaways on other blogs. It's a great resource.
Fifth, follow contest pages. One example is @giveawaynow. All they do is run giveaways!!