It really is odd to see how many of us have had serial killer obsessions. I have something similar, in that I have a great deal of interest in certain cases which haven't been solved. For instance the EAR/ONS, the Zodiac, and Jack the Ripper. I have no idea where this interest came from, but I believe that it relates to my primary obsession in some way. Here's a partial list, with the items in no particular order, except for the first one.
-Scientific Skepticism. This started as a child. An obsession with things such as Bigfoot, ESP, aliens, ghosts, etc. After some years, I realised that there wasn't actually any good evidence for any of them, and ended up going the other way. These subjects are still a very major interest of mine, but I don't accept that any of them are likely real phenomena. This would be my primary obsession. It's been with me now for about 20 years. The others on this list come and go, but this one always comes back.
-Unsolved serial murders. I believe this relates to the above, in that the underlying interest may be the mystery itself.
-Computers.
-Accents in the English language. I hear accent differences remarkably well, and am fascinated by them.
-History, covering curiously specific periods and areas
-Virology
-US politics.
-Evolutionary theory
-IRC. I've been there Way Too Long now.
-Magic. By which I mean the sleight of hand, and not the ability to hurl fireballs and turn your enemies into pigs.
-Mythology, primarily Christianity, Judaism, Norse and Greek.
Various others have rotated through in during my lifetime. These are the more recent ones.