Are student records accessible by university officials? Application forms for graduate school usually contain some vague statements regarding the extents of usage of one's social security number. 
Some people believe that educational records at other institutes are private information and the universities should have access to the educational records that the applicant would disclose to them ONLY. (Regardless of potential consequences and/or ethical justification for actions of either party.)

My question is, having the applicant's social security number, can schools see which schools/programs the applicant has attended, for how long, and the courses that were taken in the past? If so, is this a common practice? That is, do graduate offices commonly check with social security information to make sure that the records from each previously attended institute is included in the application?
The answer provided by earthling is excellent. I would like to tackle this question from another angle.

I don't believe any school will purposedly leak or illegally obtain student information. You are in the US. You are protected under FERPA.

However, accidents always happen. For example, what if one of the professors in the school you previously attended just transferred to the school you are applying. He would know you were in another school and the program you were in. Or your current advisor met with your former advisor in a conference. Academia is a small world.

I would not worry about the SSN issue if I were you. Just focus on your application and your study. Put aside your past. Pursue the future.