Hello and welcome to my User Tip
We get this question a lot, so I wrote this to assist and inform those of their options.
Your data recovery options
If your boot drive itself is mechanically or electronically dead (worst case)
Then a few thousand dollars can be spent for platter data recovery services for hard drives to dissect and recover your data (provided Filevault wasn't used to encrypt the drive). Most users don't go this route, but it is available.
Before determining that a drive is non-functioning, it will have to be removed from the machine or external enclosure (like external hard drives come in), tested and connected to other machines with special software that bypasses a lot to read the drive directly.
Also some of these very expensive data recovery services now can also recover data from a failed Solid State Disk (SSD) in addition to dead hard drives.
If the Mac or enclosure is dead, but the internal hard drive works
Then it can be physically removed from the machine and a SATA to USB adapter used to another Mac (or PC with MacDrive installed or a Linux machine) and the files recovered. Or special software used to directly control the drive to read the unencrypted bits.
Some Mac's the warranty, AppleCare or damage will occur if the drive is removed by non-certified Apple Repair folks, some will incur damage regardless as Apple likes to seal things up.
If the Mac is worthless as a functional machine, then a user can certainly use extreme methods to remove the storage drive out of it. Mac dissection videos can be found online at various Mac friendly repair and parts suppliers.
Migration Assistant can be used to migrate programs and files to a new machine if the Mac is dead, but the drive is fine using the SATA to USB adapter.
iFixit and Other World Computing
The now external drive also can be accessed directly without Migration Assistant.
You might have to select the drive and Finder > Get Info and at the bottom "Ignore Permissions on this volume"
Also you can copy and paste the locked Users folders to the new drive, using your Admin password and pick though the files.
You may need to change user permissions on all transfered files in your user account on the new external drive see #6 here
If the Mac and hard drive are fine, it's a software issue/corruption issue that's causing you not to boot or access the drive
Depending what is causing the problem it can be fixed in place, leaving your files intact. OS X (in 10.6 and above) can be reinstalled in place, leaving almost everything else alone.
Yes, it is possible to recover data off a drive Disk Utility says it can't repair, or that OS X isn't booting from.
If the only way to fix your problem is a drive or OS X partition erasure is called for, before that occurs the Mac can be booted from OS X installed on a external drive, then either regular drag and drop copy methods or Data Rescue type software ($100) can be used to direct read the 1's and 0's of bits on the hard drive (ignores file structure etc) before erasure occurs. Data Rescue type software can also be used on the hard drive if it was removed from the machine using the SATA to USB adapter.
Try the drive on other machines, see if it shows up. Don't format the drive as even if it's not showing up, data can still be recovered if it's mechanically working and the file system is not.
These more extreme data recovery measures likely will not be undertaken by busy Apple staff, that's why your supposed to make backups before trouble occurs.
Local PC/Mac repair shops specialize in data recovery efforts which fall short of expensive dissection, which is usually handled out of town as it involves expensive equipment and the high cost/desperation by the original owner to pay for it makes for few customers.
Problems reading a external drive?
The first order of business should be to disconnect all other hardware and fix the Mac itself throughly to make sure it's not the source of the problem.
Next would be to address the NTFS issue and install/reinstall that necessary software if the drive was formatted NTFS, then attempt to access the drive again.
If the drive is still not showing up, then to address that issue:
1: By attempting to connect to other machines, using other cables and ports on the Mac's, other Mac's and PC's depending upon the format of the drive.
2: If it's port powered, to use a powered USB hub as Apple is cutting off devices that are drawing too much power
3: If all those attempts fail and the drive has no encryption (Filevault), to install Data Rescue (free trial) to see if it see's the drive, if so then to purchase the software ($100) and send the recovered data to another external hard drive large enough to handle it. (formatted GUID and OS X Extended Journaled in Disk Utility)
4: Use the local services of a professional computer repair service, there might be a Linux geek there that knows a few tricks.
5: If the drive still doesn't show up, it might be a electronic issue of the enclosure/port interfaces, the internal drive can be removed and a SATA to USB adapter cable used
6: Last if the internal hard drive itself is mechanically dead, then the "4 figures" drive Drive Savers type dissection is certainly a option if the data on the drive is not encrypted (FileVault)
Determine how bad the internal boot drive problem is
You can do a few things yourself to determine how severe your problem is and even fix it yourself.
One must determine if it's a easy self fix, a more complicated (but fixable by you or others) software problem or a hardware issue (you likely won't be able to fix yourself) and if it is the storage drive or not.
Try the drive on other machines, see if it shows up. Don't format the drive as even if it's not showing up, data can still be recovered if it's mechanically working.
Run through the Steps 1 - 8 and report the results of each step in your original thread, won't harm your data.
This will tell you right off how bad it is, by how far you get in the Steps.
If you need to do data recovery
This link provides steps how to install OS X on a external boot drive and go about doing that and data recovery.
If you have another Firewire capable Mac.
Consider your numerous data backup options later
Have a plan in place before trouble occurs.
If this is all too much for you,
Consider a local PC/Mac repair as one of their main business is data recovery.
Then if your machine has a hardware problem, take it to Apple. Especially if it's under warranty/AppleCare, however they don't do data recovery and can just erase your whole drive or replace with a new one without your data.
If Apple says your machine needs a new hard drive, see about getting the old one for data recovery efforts elsewhere, or see if they will take the drive out of the machine, or will take the machine for repair if someone else removes the drive first.
Your data is usually of utmost importance, just don't give your only copy away, there are third party repair options for Mac's.
If your data is of the sensitive nature
With the new features of OS X with "timemachine local backups" and "versions" etc., you simply cannot erase files and scrub a hard drive anymore.
Certainly can't scrub a SSD at all and the NSA approved method for data destruction on any solid state drive (flash, USB thumb drive or SSD) is to grind it into a fine powder.
And for good measure you should also include traditional hard drives into that destruction because of all the behind the scenes data duplication and location tracking databases Apple is maintaining on it's users in the sake of offering new features.
Only by being able to remove the entire drive, maintaing physical control over it, is your data safe from others who may misuse it, question your ownership of media files or the nature, intention or purpose of your content.
We used to be able to safely scrub our hard drives of sensitive data, but that feature has been removed in various new features or new features added to later OS X versions that it just makes it a lot simpler to just remove the drive if your able and replace it with a new one when the machine is repaired.
If you can, take the storage drive out of the machine or have someone do it for you. You can later use a SATA to USB adapter to transfer your files to a new Mac or PC as outlined above.
Some older Mac's the internal storage is a "user serviceable part" and thus you can remove it (without voiding AppleCare or warranty) and take the machine in for service and Apple will install a new boot drive along with the repair.
Most all newer Mac's are now coming sealed up, if you open it you violate your warranty/AppleCare, which basically means your data is also trapped on the drive.
Data on iPods, iPads, iPhones and any Mac that have a Fusion Drive or it's sealed up cannot be safely deleted without destroying the entire device.
If you go ahead and open the sealed machine that can be opened or have it opened by non-Apple tech support personnel, maintain a physical presence and take possession of the drive when it comes out of the machine. If it or the computer is booted or hooked up to another machine, powered applied, your data can be copied or observed. Unfortunately since the AppleCare/warranty is violated opening a sealed machine, you will have to pay out of pocket for a new drive.
Some sealed machines can be permanently ruined if opened.
Fusion Drives consist of flash memory on the Mac's logicboard/motherboard combined with a traditional spinning platter hard drive. The flash memory portion cannot be removed or it's data safely deleted without destroying the entire logicboard which is basically the entire guts of the computer.
Deleted data can be recovered hard drives/hybrid, Flash, Fusion Drives and SSD's. Filevault is no assistance as the password is required for servicing the machine.
The encryption on iPhones is weak because of the weak passwords used.
Recent public knowledge of government intrusion into cell phones, computing devices, Internet traffic etc by the NSA and providing that information to federal law enforcement agencies was always suspected is now confirmed to be be occurring on a mass scale.
Next time when considering purchasing computing hardware, make sure the option of a user removing the storage containing your sensitive data is a option.