Hello,
I was having the same problem, with the booting process taking around 2 HOURS to even see the desktop window.
I have reviewed comments posted by some colleagues here and finally was able to SOLVE THE PROBLEM!
FILEVAULT 2 was definitely the problem (And YES, similar to other forum members here I have accepted the full system encryption during installation of Yosemite).
Steps I took:
1. Booted my Mac by holding down ⌘-R (Command –R) to boot from the Mac’s Recovery mode.
2. Selected Disk Utility and continue.
3. Selected my hard drive.
4. Under the File menu (at the top), selected Unlock “Drive Name”.
5. Then, selected Turn Off Encryption…
6. When prompted for a password, entered the password of my main account.
Then I received a warning message that the decryption would run in background and would take a long time.
7. Clicked OK and restarted my Mac.
8. The booting process was then very fast (well, I was used to the 2 hours thing!)
Then after the reboot, I accessed the System Preferences / Security & Privacy / FileVault and noted the drive being decrypted.
It took approximately 5 to 6 hours to the full process to conclude.
Hope this post can help other people solve their problems.
Important: Always have a full backup of your files. Even if you don't use time machine, do it manually. Copy to an external hard drive, to the cloud, to whatever. But do it.
Last tip: If you are having problems even to get to your files to perform the backup, you can do the following:
1) Book your Mac normally by pressing the power button.
2) Press and hold the SHIFT key until you see that the computer entered in Safe Mode.
3) Copy your files! 🙂
That's my first post. Sorry for being too long. But hope it helps folks out there.