If undergraduate Honor's Thesis printed/shelved in Alma-metar's library & checked out a number of times -- does it count as "published" on a CV? As an undergraduate, I joined the Honor's Program, and completed the program by conducting original research and writing an Honor's Thesis. That Honor's Thesis has since been printed and shelved in the library. I never included it as "published" in my CV because I didn't think that it legitimately counted as a published document. However, I have been informed that professors and students and the local public have been checking out my Honor's Thesis over the last several years. In fact, I checked the university's library database and someone does indeed have it checked out for six months. But this work is still not considered officially published? Or is it? How do I list it on my CV?
Any work that has been made publicly accessible in an archival manner can safely be considered published (along with some that are a bit more tenuous).  That includes all manner of theses, whether or not anybody is actually reading or citing them.  Thus, you should definitely list it in your CV as part of your publications.

In a typical academic CV, however, publications are separated into different categories.  How many categories depends on the particulars of one's field and record, but it typically at least divides into peer-reviewed (e.g., journal articles) and non-peer-reviewed (e.g., your thesis).  I would further recommend having a specific category for large non-peer-reviewed works like your thesis (on my own CV, it's "Book Chapters and Theses"), to distinguish them from smaller tech reports, abstracts, and the like.