Look For Regionally Accredited Universities - Regional accreditation is the most important accreditation a school can have. Make sure the school you are considering has that before you commit.
Check With a List of "Degree Mills" or Online Schools Under Investigation - There are lists online of online schools who are under investigation or have already been known to be fraudulent "degree mill" type schools. Check with this list before you decide on a school.
Avoid The Schools That Can't Get Federal Financial Aid - When a school lacks the ability to offer federal financial aid, its usually because they lack the right accreditation to do it. Costs for you will be higher if you have to finance your education with private loans.
Read Reviews About the School - There are many reviews online by students of online schools. Check those out before you commit and see what former students have to say.
Find Out The Way Classes Are Taught - When you read reviews see what people say about the format classes are taught. You can also call the school to find this out. Some online classes are completely at your own pace and others have deadlines. Some classes are offered at a certain time and place online. Others require you to work online with other students in group activities. Depending on your particular learning style, you might want to find out what format your prospective classes will be before you decide on a school.
See my list of Recommended Universities With Online Degrees.
All of the schools I have listed are "brick and mortar" schools and universities with solid reputations. They all have both on-campus and off-campus students. Visit http://www.gradwise.org for more information.