Single word for "going along with the crowd"

Perhaps you're looking for conforming:

2 a: to be obedient or compliant—usually used with to <conform to another's wishes>
 b: to act in accordance with prevailing standards or customs <the pressure to conform>

—source Merriam-Webster

Or conformity as a noun:

3: action in accordance with some specified standard or authority <conformity to social custom>

—source Merriam-Webster

A person who routinely conforms to established standards or authorities, without questioning those standards or authorities, would be called a conformist, and adopts a stance of conformism:

1. a person who conforms, especially unquestioningly, to the usual practices or standards of a group, society, etc.

—source Dictionary.com

Words to describe that behavior? I can't think of anything other than "bandwagoning" and "bandwagon effect."

Words that describe a person who engages in such behavior are much more plentiful though, and include "lemming," "sheep," or "trendster." "Yes man" might be appropriate, depending on what exactly you're going for and "fashion victim" is perfect for certain contexts.