In origami, many designs are traditional models that can't be attributed to one specific person. But, there are also a lot of new projects that are the result of the hard work of talented paper folders who generously offered to share their designs with other origami enthusiasts. If you're folding an origami Yoda or an origami Hello Kitty, for example, you can be certain that there is someone who deserves credit for coming up with the original design.
If you're folding a design and you know who created the model, it's considered common courtesy to credit that person when you're sharing your work in any sort of public forum. You should give credit even if you're not receiving any sort of payment for your work. It's a sign of respect for your fellow paper folders.
It's not always easy to locate the creator of a model, thanks to the social nature of the Internet. Photos of popular designs can be shared thousands of times in just a few hours, making the original source less obvious. Fortunately, many of the more established origami artists do have websites, blogs, Facebook profiles, and other means of communicating with their fans. With some digging, you have a decent chance of finding the creator of a particular project.
Origami artists, like artists in general, are generally fairly reasonable people. However, trying to pass off someone else's work as your own is not going to win you any admirers. Making an effort to give credit where credit is due, on the other hand, displays thoughtfulness and a sense of personal integrity.