I am just starting my online RN to BSN program, and I still have clinicals I have to do and arrange on my own. I took many of my liberal arts co-requsites for my ASN online, like Human Development, Cultural Anthropology, Western Civ.
If what you're looking for is a totally online RN program with no nursing license yet , I highly doubt there is such a thing, and if there is I would be very careful with it. Nursing school has a lot of clinical and lab time and you would need to have a clinical instructor with you at any time in clinical. But many schools offer or are starting to offer more online courses and "hybrid" courses with less on campus time and an online component.
As for accreditation, there is regional accreditation and many other types. See:
http://ope.ed.gov/accreditation/Search.asp
And check out allnursingschools.com too.