Yes
For example, this is my current user agent:
Mozilla/5.0 (X11; Linux i686) AppleWebKit/537.36 (KHTML, like Gecko) Chrome/32.0.1700.102 Safari/537.36
The components of this string are as follows:
Mozilla/5.0
: Previously used to indicate compatibility with the Mozilla rendering engine
(X11; Linux i686)
: Details of the system in which the browser is running
AppleWebKit/531.21.10
: The platform the browser uses
(KHTML, like Gecko)
: Browser platform details
Chrome/32.0.1700.102
: Information about the browser.
In short, there's in the above user agent string that's really unique to me. If a different person on the Internet with the same configuration accesses your website, then their user agent will be the same.
See RFC2616
for more information about the structure of User-Agent strings.