The major national accreditation bodies for nursing schools are the NLN/NLNAC (National League of Nursing Accrediting Commission) and the CCNE (Commission on Collegiate Nursing Education). Almost all employers (especially hospitals) require their nurses to have graduated from a school with accreditation from one of these bodies. Some states even require that the school be accredited in order for the graduate to sit for NCLEX.
Then there are state accreditations and other, lesser known accreditation bodies. These allow schools to say that their nursing programs
are accredited, but without having to maintain the higher standards of the major accreditors.
Really, one of two things will happen if you go to a non-accredited (or not accredited by the NLN/CCNE) school. 1. You'll have no problems, graduate, pass NCLEX, and find a job right away. 2. You'll graduate and then hit lots of roadblocks either when applying for licensure, seeking endorsement to another state, and trying to find a job because your school wasn't accredited.
In my opinion, it's not worth the risk and if your school isn't accredited by either the NLN or the CCNE, you should seriously think about finding a different school.