How to behave when dating a fellow PhD student in same department? I am currently dating a PhD student in the same department as me (I am also a PhD student). Not the same research group, but closely related topics anyway. We're both happy with it, and I don't think there's anything wrong with it, but I am worried about possible negative consequences on the job.

So, what rules (written and unwritten) should be followed when dating someone like that? that is we do not work together everyday but we are still working closely, both geographically and scientifically.
One possible thing to watch out for: in some departments, graduate students may work as teaching assistants for graduate courses.  You should ask not to be assigned to TA courses which your significant other is taking (and he or she should do likewise), as this would represent a possible conflict of interest.  Even if you can grade your SO's work objectively, there might be a perception of unfairness among other students.  Likewise, if any other situation should arise where one of you might be in a position of authority over the other, you'd need to disclose the conflict of interest and be prepared to resolve it.

Otherwise, as Peter Jansson said, relationships between graduate students are very common and aren't likely to cause academic concern.  Just stay professional about it (e.g. don't make out in the hallways).