Bookshelves and other furniture must be removed to do the job. Several homeowners and contractors swear by a relatively new technology that can save the headaches, as well as thousands of dollars. It involves injecting liquid glue under the floor. The trick for the homeowner is to detect loose tiles early, since floors in the final stage of failure must be removed and reinstalled. The earliest stage can easily be detected by tapping on a floor with a broom handle.
Loose tiles give off a distinct hollow sound, compared to their solid counterparts.
The second stage of failure shows up as cracks in the grout. Injection won't help those floors but it can help floors caught in the first two stages. It's like a disease. When the glue is completely under the tile, it squirts out holes drilled in the grout on the other side. I wasn't sure it would work, but it's been in there five years and it works perfect.