I included emoji in my password and now I can't log in to my Account on Yosemite

If you have "Other Input Sources" available at the top right of your login screen, select the one called Unicode Hex Input. This can be used to input emoji (or any other character) into the password field, as long as you know the Unicode Hex number of the character. This number can be found in the Character Viewer or on the internet.

Some items you find in the "emoji" category have Unicode hex numbers with just 4 characters, such as Airplane U+2708 ✈. With the Unicode Hex Input keyboard, you input this by holding down the Option key while you type 2708.

Other emoji have Unicode hex numbers with 5 characters, such as Grinning Face U+1F600 😀. For these you need to find the two corresponding UTF-16 Hex codes (sometimes called "surrogates") by consulting Character Viewer or using an internet source like fileformat.info. For 1F600 these are D83D and DE00. You can input 1F600 by holding down the option key while typing D83DDE00. You may see two dots in the field, but it is still just one character.

I solved it by the solution Apple Support suggested to do, here are the steps I did:

1. Install OS X on an external drive from Recovery mode (Cmd + R while starting).
2. Boot from the external drive.
3. Install the Hex/Emoji keyboard to be able to type the relevant character.
4. Go to Disk Utility, choose the locked disk. Go to File -> Turn Off Encryption.

5. Enter your password here and leave it for couple of hours, since the decryption is going to take a while and there is no indication of progress.

   

6. Restart in Recovery mode again. Go to terminal and run resetpassword.

7. Choose your disk and create a new password for your user.
8. Restart and use your brand new password to login.

Since you have Filevault - that makes your situation precarious and a bit delicate.

Some good news, Apple has disabled emoji entry in the password pane for 10.11 El Capitan - I can't paste or get emoji in the Users & Groups preference pane.

Apple's official manner to get past this is to click the ? in the password field and reset your password. If you used a recovery key - you can enter it without needing emoji keys. If you used AppleID, you can enter that without needing emoji.

Barring that, If you have a current backup (or can let things complete if you are logged in), the fastest way froward is to wipe the Mac and then restore the backup. You can choose a new password for a new admin account and then import the user files.

If you have ssh enabled, or remote desktop enabled, and the Mac is still logged in to your account, you could log in to the Mac from another Mac over the network. This will not work if you have rebooted the Mac and Recovery HD boot is waiting at the Filevault unlock screen.

If you have a second admin account that is FileVault enabled, you could reboot and use that password to unlock the disk and then reset the password on your main account. Lastly, you could boot to recovery HD or internet recovery and reinstall the OS to a USB drive. Then you can mount the file vault drive and have emoji to unlock the volume and make a new admin account through various tricks / procedures similar to using single user mode to remove the .AppleSetupDone file.

Adding to bmike's answer, if you can't do any of that, and don't have a recent backup, you might try connecting the disk to another computer, and mounting the volume to save your files. You can apparently do it with both mac, windows and linux.