Thesis Option: You have to work on a specialized project or topic for the completion of your degree. This will involve some research in your domain of study. You will work with a professor to complete your research. In some schools you will get Research Assistantship easily if you choose Thesis option for MS.
Non Thesis Option: Thesis option in Masterís Degree involves a mini project or a comprehensive exam to complete your degree. Comprehensive exam is nothing but an exam conducted by university after completion of certain courses in your degree.
Advantages of Thesis Option:
1) Research at masters level will make your application strong for PhD admission
2) Makes your resume strong for job search.
Disadvantages of Thesis Option:
1) Will take longer to complete the masterís degree since it involves research. Usually masterís degree with Thesis option may take over 2+ years.
Advantages of Non-Thesis Option:
1) You can complete masters degree in short time.
2) No need to put effort on research.
Which one to select for MS in US?
I personally prefer Non-Thesis Masters option, because one can complete the degree in short time and can start job search. If you are really interested in research or want to Join PhD course, select the Thesis Option. Sometimes you will choose Thesis option to get the Funding / Assistantship from the university.
When should i select Thesis or Non thesis options?
Some schools will ask you while filling the application for admission. Some may ask you after joining the school.
Is it mandatory to select Thesis Option?
In Some schools it is mandatory.