Yale is accredited by the New England Association of Schools and Colleges (NEASC). Charter Oak State College is accredited by the same body. Ohio State is accredited by the Higher Learning Commission of the North Central Association of Colleges and Schools (NCA/HLC). Excelsior College and Thomas Edison State College (and Cornell University, as another example) are accredited by the Middle States Association of Colleges and Schools. All of these accrediting bodies are recognized by the United States Department of Education Council on Higher Education Accreditation (CHEA).
As for your master's degree question, the issue isn't really
transferring of credits (the credits you have earned will have been presumably already applied to your bachelor's degree), but rather being accepted to the master's program you're interested in. Every program has its own criteria for acceptance, but typically they are looking for a bachelor's degree from a regionally accredited college or university -- and all of the "Big Three" pass that qualification.
For comparison, consider
California Coast University. They are accredited by the Distance Education and Training Council (DETC). This is often referred to as "national" accreditation. The DETC is also recognized by the Department of Education CHEA, but many (most?) master's programs do not recognize DETC accreditation at this time. Do some Googling if you're curious about the reasons why.
By the way, I don't mean to knock CCU or DETC-accredited schools generally -- I have heard good things about several of them.
Maybe I'll post again later about unaccredited schools and diploma mills. It can be fascinating to look around at what's out there.
-Gary-