Not seeing my HD in the disk utility I tried to start up my computer and got a flashing file with a question mark. 
So I held down the ⌥-key on boot and brought it into recovery-mode.

After going through the different options I went to the disk utility and all I see is the grayed out SuperDrive and below there is disk0 and Mac OS X Base system. 

Leaving disk utility I went to reinstall Mac OS X. After the verification and agreeing the terms, it doesn't show my harddrive. 

Did I unmount the harddrive or what could the reason it's not showing up?
I am assuming that you got a flashing folder with a question mark similar to this:



That means your Mac cannot find the boot loader.  

Now, since you said that you were able to go into disk utility, you already know how to boot into Recovery Mode.  What I am assuming you saw when you were working in Disk Utility is something similar to this:



The SuperDrive being greyed out is probably because the drive is empty.  disk0 is typically the disk drive in your Mac.  Mac OS X Base System is more than likely a partition on disk0

Do this:

Hold down the Option while powering on your Mac.  If there is a bootable partition, it will be listed (other than the recovery partition).  If so, boot into it.  

Once you have booted, check to see what you have selected as your startup disk (Preferences --> Startup Disk)