Here are common iTunes error when trying to restore your iPhone:

Error -1 Error occurs when one uses the “last ditch” method for preventing baseband updates on the iPhone 4. The baseband does not get updated using this method. Use TinyUmbrella to kick it out of recovery mode.

Below 100
Error 1

• You are attempting to downgrade an iPhone from iOS 5 to iOS 4.x. To resolve, use either custom firmware created by PwnageTool/sn0wbreeze or use notcom’s FixRecovery utility available on his site.
• On an iPhone 4 downgrading from iOS 5, use the option in TinyUmbrella to allow a baseband “upgrade” to bypass the error and go back to basband 04.10.01.
• Unable to downgrade. Try changing the USB port (the back one of chassis is better) and restart computer.
• The installed version of iTunes may also be too old. Update iTunes.

Error 2

• ASR does not exist on ramdisk or is corrupt/not signed.
• sn0wbreeze 1.6 Custom Firmware has a ASR patch problem. Use sn0wbreeze 1.7+ or PwnageTool. Device isn’t bootable.

Error 6
Not enter the downgrading mode, change USB port (the back one of chassis is better) and restart computer.

Error 9

• Due to asr being patched, the SHA signature is automatically changed and after being resigned the kernel will refuse to use it. Therefore proper kernel patches are required. If necessary kernel patches are not applied, it will fail to load asr and error 9 would occur during restore.
• Rebooting your Mac or PC may resolve this issue.

Error 10 LLB is missing from the IPSW. The device cannot be booted up. The trick to skip the baseband update no longer works.

Error 11

• Removed BBFW file in the firmware folder of an unzipped IPSW. Can also be used to prevent a baseband update. The device is bootable, if you set the auto-boot to true or use TinyUmbrella and use “Kick Device out of Recovery”.
• You are trying to update to a custom firmware from PwnageTool 4.1+. You always have to go into DFU mode and restore from there.

Error 13

• Occurs when you want to install a beta firmware with iTunes for Windows (actively blocked by Apple; beta users are developers and therefore must have a Mac).
• USB problem. Check the USB connection and try other direct ports or maybe the USB cable is an older one. Device isn’t bootable.
• The installed version of iTunes may also be too old. For firmwares 4.0 and higher you need iTunes 9.2 or higher. Update iTunes.

Error 14

• Custom firmware update fail (PwnageTool until 4.0.1). You have to restore the device with a custom firmware. Update to a custom firmware isn’t working. Device isn’t bootable. 2
• USB Problem. Check the USB connection and try other direct ports or maybe the USB cable is an older one. Device isn’t bootable.
• You’re trying to ‘update’ to a beta firmware instead of performing a restore. Device is still bootable if you kick it out of recovery mode.
• Rebooting your Mac or PC may resolve this issue.
• Root file-system partition size was set too small in the ramdisk’s options plist.

Error 17

• Device failed to display the applelogo img3 which results in this error.
• One or more of the nand0/nor0 flash images were missing from the IPSW.

Error 18 This occurs when the media library on the device is corrupt and cannot be modified or updated.

Updating to the latest version of iTunes and then restoring should resolve this issue

Error 20 Reportedly happens during failed downgrade attempts (iOS 2.0 to 1.1.1, 5 beta to 4.3.3).

Some have seen success afterwards by doing the downgrade from DFU mode instead of the normal Recovery mode.

Error 21

• Custom firmware restore fail (PwnageTool since 4.1). You have to put your device into the DFU mode and not into recovery mode. Device won’t boot correctly an stuck at the Apple logo after the error. Press and hold power and home button until it reboots.
• Error when using Sauriks server for a restore with iOS 5.x in the recovery mode at least on a A5 device.

Error 23 Cannot restore or update due to hardware problems.

• In software you have to set default web browser.
• In hardware, it’s a communication problem. Check all connections, also try to change battery.
• Faulty baseband flash or processor
• Happens frequently after water damage. Remove and clean motherboard.

Error 26

• Values or variables in the options property list within the ramdisk are incorrect.
• False version of the NOR flash firmware. Use the correct sn0wbreeze version.

Error 27

• I got this after I tried to flash iOS5 from 3Gs on a 3G Phone (I modified the restore.plist so it would flash and also exchanged RestoreRamDisk and kernelcache)

Error 28

• Hardware error. Return your device to Apple if possible. The problem is a bad dock connector on the iPhone. Must change the connector.
• If you have tried almost everything, reset the logic board (leave uncharged for five days or remove battery for half an hour), then pwn and restore. If this doesn’t work, the flash memory/hard drive of your device is damaged.

Error 29 See Apple’s discussion thread number 2329795 about this problem. You might need to change the battery.

Error 31 Main Article: DFU Loop

Error 34 Hard disk is run out of space when trying to download. Clear space and then continue downloading.

Error 37

• iPod touch 2G LLB patched with the 0×24000 Segment Overflow was used on an iPhone 3GS custom firmware. Known on damaged bundles from unofficial PwnageTool distributions or bundles.
• sn0wbreeze 2.0.1 bug, which was fixed in 2.0.2.
• Recent sn0wbreeze can cause this issue. Deselect all custom boot logos, recreate IPSW. If received on an iPhone 3GS, select “new boot-rom” and deselect all custom bootlogos, then recreate the IPSW.

Error 40 Hacktivation bug in Sn0wbreeze 2.0.1, which was fixed in Sn0wbreeze 2.0.2.

Error 46

Errors 10xx
Error 1002 Error when restoring.

Error 1004 This is caused by a failure to match the Baseband Nonce currently in memory to the nonce returned in the Baseband Firmware SHSH blob. This happens if you edited the hosts file (Saurik’s Server) or you are using TinyUmbrella. Use TinyUmbrella and “Kick Device Out Of Recovery” to boot. 1

Error 1011 This is caused by recovery mode being in userland (1.1.1 firmware). The file iTunesMobileDevice.dll is damaged or updated.

Error 1013

• iPhone 4
  • This means that the baseband did not get updated. Either remove the gs.apple.com entry from your hosts file and let the baseband upgrade or if you want to preserve the baseband just jailbreak at this point to boot it up.
• Other Devices
  • Restart computer; change computer; reinstall system, if the device is always in restoring mode: XP users can jump from restoring mode with ibus; MAC users can use iNdependence. (usually on the iPhone 2G with 1.0.2 firmware downgraded from 1.1.1)

Error 1014 This occurs when you try to downgrade your device’s baseband.

Error 1015 This error is common when downgrading iPhones and 3G-enabled iPads. The problem occurs when the device’s baseband has a higher version number than the baseband in the firmware you restored to. Just set auto-boot true in iRecovery or use iREB/TinyUmbrella/RecBoot.1 In case this is not working use Pwnage Tool to create a custom firmware WITHOUT the iPad baseband, put your device in pwned DFU mode and restore via iTunes.

Errors 13xx
Error 1394 When Spirit2Pwn flashes parts of the boot chain on iOS 4, the device may crash into DFU Mode.

Errors 14xx
Error 1413 Restart computer; change USB port; reinstall system. See also Apple’s Knowledge Base article number TS1927.

Error 1415 Restart computer; change USB port; reinstall system.

Error 1417 Restart computer; change USB port; reinstall system.

Error 1418 Restart computer; change USB port; reinstall system.

Error 1428 Restart computer; change USB port; reinstall system. (downgrade from www.iphonebus.com)

Error 1050 Bad response from gs.apple.com OR need iREB for preparing the device for restoring to custom IPSW

Errors 16xx
Error 1600 - Custom firmware can’t be restored on a device with DFU Mode. The software of the iPhone isn’t patched. Using iREB, sn0wbreeze, redsn0w, or PwnageTool, you need to enter a pwned DFU Mode. During that process the software gets patched and the custom firmware should run without any problems.

- APTicket problems if you try to restore to iOS 5.x in the DFU Mode.

Error 1601 See also Apple’s Knowledge Base article number TA38633.

Error 1602

• Restart computer; change computer; reinstall system.
• If this error occured during an Apple TV restore, then unplug the Apple TV from the power cable, after you entered the recovery or DFU mode, and then try it again.

Error 1603 False kernelcache patch. Known on damaged bundles from unofficial PwnageTool distributions or bundles. See also Apple’s Knowledge Base article number TA38604

Error 1604 Device was not pwned (signature checks were not blocked). Custom firmware can’t be restored. Can also happen when there’s a problem with the IPSW.

Error 1611 iTunes tried to enter the Restore Mode, but the device turned back to the Recovery Mode. This can happen when updating an iPad 2 jailbroken with Saffron gets updated to iOS5. In this case simply retry, as it is in Recovery Mode then anyway.

Error 1618 Missing system files or corrupt data in iTunes installation. Try to uninstall iTunes, restart computer, install again. This error also occurs for iTunes in Windows 8 for reasons currently unknown.

Error 1619 iTunes is too old and couldn’t read the iPhone in Recovery or DFU Mode. Please update iTunes and try it again.

Error 1644 IPSW was moved during prepare with iTunes. Try it again and don’t move the IPSW.

Error 1646 iTunes expected the device to be in a different state (Example: booted into iOS rather than jumping to iBEC).

Errors 20xx
Errors 2000-2009 (from Apple support): If you experience this issue on a Mac, disconnect third-party devices, hubs, spare cables, displays, reset the SMC, and then try to restore. If you are using a Windows computer, remove all USB devices and spare cables other than your keyboard, mouse, and the device, restart the computer, and try to restore. If that does not resolve the issue, try the USB issue-resolution steps and articles listed for Error 1604. If the issue persists, it may be related to conflicting security software.

Error 2001

• The Mac OS X kernel extension “IOUSBFamily” that was bundled with late 2008 / early 2009 MacBooks, as well as the 10.5.6 update, has a bug where it fails to properly recognize an iDevice in DFU Mode. It can be resolved by updating to 10.5.7 (or later), or using a USB hub.
• Close limera1n.

Error 2002 iTunes can’t connect because another program is using it or it’s disconnected during the Apple Server check.

Error 2003

• Connection problem; change USB cable and check USB port.
• sn0wbreeze failed to restore IPSW; unplug and plug iDevice and try again

Error 2005 Problem connecting. Probably a hardware failure.

Somebody reported that reinstalling the USB drivers fixed the problem.

Error 2006 Replace the USB cable with a newer one and/or disconnect all other USB devices, then retry.

Error 2009

Errors 30xx
Error 3002

• Update to an older firmware isn’t working, because Apple is no longer handing out SHSHs for the device/firmware combination.
• Or a timeout checking Apple server – retry later.
• This error also happens if you try to Update with a local TSS server (TinyUmbrella tool) and probably also when connecting to Cydia Server. Use Restore instead.
• Error 3002 represents no update ramdisk when pressing Shift+Check for updates.

Error 3004

• No internet connection during the firmware restore.
• iTunes can’t connect to gs.apple.com. Maybe Port 80 and Port 443 is blocked. Open it on your router.

Error 3014

• Bad hosts file. The SHSH request couldn’t be completed. No connection to the Apple Server, Cydia Server or localhost (for TinyUmbrella.
• iTunes can’t connect to gs.apple.com. Maybe Port 80 and Port 443 is blocked. Open it on your router.

Errors 31xx
Error 3123 Something dealing with movie rentals.

Error 3191 QuickTime may be corrupted. You must reinstall it before iTunes will work. Windows users, also try turning off Compatibility Mode for QuickTime.

1. Right-click on “C:\Program Files\QuickTime\QuickTimePlayer.exe” (“Program Files (x86)” for 64-bit Windows) and choose Properties from the shortcut menu.
2. In the Properties window, click on the Compatibility tab. Deselect the checkbox labeled “Run this program in compatibility mode for.”
3. Click Apply.
4. Close the Properties window

Error 3194 Occurs when trying to install an old firmware and Apple’s server disallows the installation. The only solution is to have SHSH backup and modify the hosts file to point to Saurik’s Cydia Server where they are backed up (or localhost if you have it yourself).

Error 3195

• There is no SHSH for the firmware.
• This is the same as “This device isn’t eligible for the request build.” but with an cache error.

Errors 32xx
Error 3200 You are trying to update to iOS 5, when infact, the IPSW file has only a Restore Ramdisk.

Courtesy of The iPhone Wiki.