What is the logind process, and why is it running? I've recently noticed that a new process is up and running every time I start my computer - logind, running as root.

I'm unsure why this is happening - could it be a patch or so? I'm running a fairly vanilla version of OS X 10.8.4
logind is a normal part of OS X. As @mt_ mentioned, there is a trojan that mimics it, but seeing a program by that name is entirely normal, not an indication of any problem.

If you are concerned that the normal logind has been replaced by a trojan, check /System/Library/LaunchDaemons/com.apple.logind.plist, and make sure it refers to "/System/Library/CoreServices/logind", NOT "/usr/sbin/logind". See the CNET article for more info.