Copyright
Copyright is an issue of increasing importance to origami designers, as well as authors and professionals who use origami to earn a living. In the good old days, origami was an obscure art and the only issue that really mattered was who came first. Authors from within origami were generally respectful of a model’s ownership, but some people felt at liberty to help themselves to designs, treating every model as if it were traditional. The Internet makes scanning diagrams and publishing (or even selling!) them online very easy.
There are precious few legal precedents to establish exactly what you can and can’t do with origami designs, but in general, there are no restrictions on folding or displaying a model in a non-commercial way. If you want to sell origami, or fold it for money, you must either use your own creations, or seek permission from the creator.
Few people would quibble about making a diagram of someone else’s work for your own personal use, but that doesn’t mean you can distribute it freely. You can do as you please with your own design – many creators publish their models on the Internet for others to enjoy. You may be unlucky enough to find that someone else created an almost identical model before you, but providing that you didn’t knowingly copy it, you should be OK. In the end, it’s a matter for your conscience.