I seem to waive my "I hate research" rule under one condition: when I research a story I have no intention whatsoever of publishing. I assume I will research in those instances because I don't worry about being completely accurate. I'm going for flavor, not fact, and since no one else will read it, no one else will know where I'm wrong.
For my Xmen short story, I pulled out maps of North America and New York to set the scene (I didn't have Internet at the time). It led to part of the story taking place on a train on the way to Canada. I would never have done that without the research.
I have a serial story line inspired by Voyage to the Bottom of the Sea. That was a terrible show for many reasons (I've posted about it somewhere), but I watched it when I was very young and it gave me some great ideas for characters and story lines (surprised me, too).
So I ran searches about owners of nuclear submarines, ports for nuclear submarines (and naval bases in general), crew compliments for nuclear submarines, schematics for nuclear submarines - it's a wonder the FBI didn't show up at my door. Or Homeland Security. Yes, I'm just paranoid enough to believe such searches are monitored. Fortunately, my nuclear submarine searches didn't segueway into nuclear bomb searches, so I'm probably good for now. Plus, I live in Kansas. Now if I purchase tickets to one of those places...
I have another serial where I need an isolated location with a population of 30-50K (not easy to find with a search engine, by the way), somewhat advanced medical facilities and no interference from US military for at least 24 hours. I'm thinking Mexico. It's close and I have a chance to use a little of that Spanish I'm learning in the dialogue. I don't want a real city, but I'd like to put my fake city somewhere reasonable, so I search for Mexico hospitals, which seem to fall into the categories of cancer and plastic surgery and oddly enough be located within walking distance of the US/Mexico border (this is listed as a positive in the ads). I did a thorough spyware cleanup after those sites, let me tell you.
I'd like a "shady element" in the story, so I look for cannabis and opium densities and put those next to cities of appropriate size and population density. If you didn't know what I was doing and only looked at my browser history, you'd think I have 4th stage cancer and want alternative healing methods and medicinal marijuana to deal with it. I'm thinking Mexico is the place to go should that ever happen.
I suspect most writers have some interesting history on their browsers.
What's your oddest search?