DuckDuckGo offers something that Google, bing, Yahoo!, and all other search engines don't; Privacy. It gives a feeling of total security and comfort. Even if you aren't searching for something that is sensitive or private, do you want a major corporation to have a total list of the links that you clicked and your searches? Do you like it when there is that annoying kid from school on top of you looking over your shoulder? "What'cha typing?". The only difference between the annoying kid and Google, is that Google doesn't have to ask. It has it all on file and some possibly rogue employees are just waiting to read it.
Google: Someone is always looking over your shoulder.
DuckDuckGo: It's you and a computer. No one can see what you are doing.