WordPress version: 3.3.2
Overview: Moving WordPress site to new server. Created brand new database, imported old SQL file into new database, FTP’d WP 3.3.2 files to server and crossed my fingers.
Problem: Home page showed up just fine, but posts and inside pages all went right to File Not Found 404 pages. Sad-face.
Solution: I went to Admin > Settings > Permalinks and simply clicked “Save Changes.” I didn’t change any of the setting, I simply clicked “Save Changes.” Voila, it all worked out!
Note: this is my personal experience with this particular situation, and I’d read about this technique over the years. Your mileage may vary.