I love getting the harder questions. For example, they'll know part of the title, but not the author. Or, they'll think they have the right author name, but aren't even close.
Today, I got to dig up several movies for a patron. Those were easy, since she had the titles and the production company.
The hard one came later. She came up with a request for a book she'd checked out and recently returned. It had a certain word in the title. I found it and made her day, since it was checked in!
The really fun ones are "an encyclopedia of criminals published in the early 1930s". Ones that are that obscure I don't always find, but I do my best. I'll utilize all of my resources, from blogs, to google and to rare book websites (and, of course, Amazon). 80% of the time I can find what they're looking for.
Usually, just googling it gives me what I want. If not, then I'll move on to Amazon. If not Amazon, then I usually have to take down their information to call them back to search for it more thoroughly.