Can I bring home-burned video discs to Ecuador?

You may bring in your DVD's to Ecuador since they are not on the prohibited list.

Be prepared to answer questions from U.S. Homeland Security before leaving the United States if the sheer bulk of the DVD's attracts their attention.  They have no cause to stop you from bringing DVD's into Ecuador provided you are not engaged in any activities detrimental to the U.S.

cccmedia in Quito

Thank you cccmedia,  Also how can I get a list of prohibited things?  I'd appreciate it.

According to the U.S. Department of State:

Ecuador's intellectual property regime is governed by the 1998 "Law on Intellectual Property." The law is intended to provide criminal and administrative relief to right holders. Ecuador has ratified the Berne Convention for the protection of literary and artistic works, the Geneva Phonogram Convention, and the Patent Cooperation Treaty. Ecuador is also bound by Andean Community Decisions 345, 351, and 486. Decision 486 improves intellectual property protection by expanding the definition of patentability and strengthening data exclusivity provisions. Ecuador is not a party to the Madrid Protocol on trademarks.

The Ecuadorian Intellectual Property Institute (IEPI) was established in January 1999 to handle patent, trademark, and copyright registrations. Ecuador has been on the Special 301 Watch List of the Office of the United States Trade Representative since 2003. Enforcement against intellectual property infringement remains a serious problem in Ecuador. The national police and the customs authority are responsible for carrying out IPR enforcement orders, but enforcement of court orders can be problematic. There is widespread local trade in pirated audio and video recordings, computer software, as well as counterfeit activity in brand name apparel. On the other hand, local registration of unauthorized copies of well-known trademarks has been reduced.

A large numbers of copies of trademarked music and other content opens you up to seizure of the materials and potentially a lot of questions on both ends of your trip.  You're tempting agents to hassle or arrest you in my opinion.