Do people really steal invention ideas?

Unfortunately it happens all the time. Probably one of the most famous cases involved the invention of intermittent windshield wipers - luckily the inventor obtained a patent, and yet just about every major automotive company adopted the wipers on their cars without paying the invention a royalty or license fee. He sued and won but it took him literally decades to go through all of the appeals - I believe - I may be wrong - but I believe that eventually he died and his estate carried on the litigation - virtually every automotive company had to pay. So, one of the best ways to protect yourself is to file a patent application and seek a patent - you can initiate the process with a provisional patent application but it must be perfected within one year of the filing date of the provisional application by the filing of a non-provisional or PCT application. The main reason to obtain a patent is that it is an official document - it will obviously not necessarily prevent litigation, as I alluded to hereinbefore, but I believe that it is stronger than a simple NDA or other agreement.
Consult a patent professional.