PhD - Doctor of Philosophy. The highest academic degree in most fields, not just philosophy. Usually takes about 10 years after high school including the bachelor's degree and often a master's.
AS - Associate of Science. The lowest "degree" level usually conferred by a community college after 2 years of full time study. Can be in an academic or vocational field.
MS - Master of Science. An advanced degree in a specialized field of study above the bachelor's degree. Usually takes 1.5 - 2 years full time after the bachelor's degree.
MBA - Master of Business Administration. A master's degree (higher than the bachelor's degree) that prepares managers and business leaders at a high level. Usually takes 1.5 - 2 years full time after the bachelor's degree and sometimes 3 years depending on the program.
BS - Bachelor of Science. Commonly called "a 4-year degree" because it takes about 4 years after high school if you attend full time. Reality is that most people take longer with the average time now nearing 6 years.
DO - Doctor of Osteopathy. A professional degree in the medical profession generally considered equal to the MD but concentrating less on medications and more on the whole body. 4 years after the bachelor's degree plus an internship and residency. About 10 years total after high school.
MD - Doctor of Medicine. A professional degree in the medical profession held by most of the people you refer to as "doctor". 4 years after the bachelor's degree plus an internship and residency. About 10 years total after high school. For some specialties it can be even longer.
MA - Master of Arts. Similar to the Master of Science but more theoretical (the MS is generally more practical or "how to") and taking about the same amount of time as the MS - 1.5 - 2 years after the bachelor's degree.
* Associates degrees - AA, AS, AAS, AFA, ASN, ABA, etc...
* Bachelor's degrees - BA, BS, BFA, BMus, BBA, BComm, etc...
* First Professional Degree - MD, JD, DVM, DDS, DO, DPharm, etc... [see note below]
* Master's degree - MA, MS, MBA, MHA, MSW, etc...
* Specialist degree and Certificate of Advanced Graduate Study (CAGS) - EdS in education/teaching. Simply "certificate" or "additional study" in other fields.
* Academic Doctorate - PhD, EdD, DMus, DArts, etc...
At the same level, there is no heirarchy of degrees. An MA, MS, MBA, MLIS, etc... are all "a master's degree" - but, there are significant differences in what each degree covers.
note: while holders of a first professional doctorate are called "Dr.", if they return to school for a higher degree it's for a master's degree (such as a JD returning for the higher degree LLM). For this reason, many people list the first professional doctorate immediately after the bachelor's degree and below the master's degree. In terms of earnings, these degrees generally pay higher than any other though.
Add: In academic terms, a theoretical degree is all about who, what, when, why of a subject and less about "how to". In this usage, a theoretical engineering degree would be pretty useless or at least called "historical preservation" and not engineering. This is why some people consider an MS to be "more practical" than an MA since the theory learned in the MA is often referred to as "book learning' but you don't know how to DO anything" while the applied methods of the MS is sometimes referred to as "can do it well but doesn't know why"