If it is, why? Have you had experience with any problems arising from attending a school that was not accredited? Share your experience.

Yes, this is very important! If you attend a non-accredited institution of higher education (IHE), while they will take your money and may give you some assignments, you will not be able to go to the next level, i.e. Bachelor's to Master's or to a Doctoral program.
If you are able to go forward--usually within the same IHE you will still have degrees that will mean nothing, will not get you through job interviews, and can cause you to loose a high level job that you've worked hard to achieve. One example was a Deputy CIO at the Dept. of Labor had a real A.A. from Rutgers University and a B.S., MS and Ph.D. from Hamilton University which is in a garage in Wisconsin it turns out!! She didn't realize this but was fired from this very responsible and high paying position. She'd had to pay $4,000 and write a 10 page paper, but that is not nearly what a real degree from an accredited university would require.
The six regional accreditation Commissions visit their region's institutions every 10 years and check about 10 areas over a two year period such as the library, student counseling, budget and services, and academic quality. The U.S. has this protection--so always check. Most IHEs post this on their home page and are very forthcoming in answering questions. If they are NOT it is a red flag. National accreditation for training or cooking schools is NOT the same thing. Good luck--but choose carefully so you have an earned degree that will last you a lifetime.

Yes because online high school accreditation is designed to protect the public: students, schools, and employers. Accreditation ensures online high schools are educating students while meeting the highest quality educational standards.