0001 power supply problem
0002 Network Interface problem
0003 Power problem could be the PSU could be the GPU/CPU, somehow the console isn't getting clean power from the power supply.
0010 over heating
0011 over heating - If you are receiving this error after disassembling your console make sure to all 8 of the heatsync screws are tightened securely to the board/heatsink holes.
0012 over heating
0013 over heating
0020 (Not yet known, possibly overheating)
0021 DVD Drive Time out - Can be caused by problems with a firmware flash. This is also speculated to sometime be caused by a problem with the southbridge chipset on the motherboard.
0022 GPU Error / GPU Overheating
0023 (not yet known)
0101 (not yet known)
0102 unknown error
though it's most likely GPU related literally means the console does not know what is wrong. possibly a short or cold solder joint somewhere. So far there is 1 major theory for what causes most of these errors is that the Ram, CPU, or GPU are not soldered properly to the mother board due either to poor manufacturing or excessive heat up and cool down cycles that stress, weaken and eventually break the soldered connection.
There are two theories to fixing this one deals with the "X" clamps that hold down the chips. The other involves re-Heating the chips. DO NOT attempt either of these if your console is still under warranty. If your console is still under warranty return it to the store where it was purchased or call MS to have it replaced. I have also heard of limited success by simply switching the AV cable from "HDTV" mode to "TV" mode.
0103 CPU Error/ CPU Overheating - see solution for error 0102
0110 Memory Error / Memory Overheating - see solution for error 0102
0200 (not yet known)
1000 (not yet known)
1001 (not yet known)
1002 (not yet known)
1003 Hard Drive Error... It could be a problem with the Hard Drive itself or a problem with the internal connection to the hard drive, Try removing the hard drive and playing without it
1010 Hard Drive Error, Can be caused buy a corrupt or missing eProm.
1011 (not yet known)
1012 (not yet known)
1013 (not yet known) possibly a dashboard update error
1020 (not yet known)
1021 (not yet known)
1022 AV cable error... There is a problem with the AV cable, try using a different AV cable. (could also be a problem with the encoder chip)
1023 DVD drive not connected, connect DVD drive to boot
1030 (not yet known)
1031 (not yet known)
1032 (not yet known)
1033 (not yet known)
1444 and up There is no "4" in the error codes four lights is a "0" go back and check your code again.

turn the xbox 360 on, and wait till the 3 red lights are flashing.
Press and hold the sync up button (the small white one), while holding that button press the eject button.
The LEDs will now blink the first number in the code (as described below).
Release the eject button and press it again.
The LEDs will now blink the second number of the code.
Release the eject button and press it again.
The LEDs will now blink the third number of the code.
Release the eject button and press it again.
The LEDs will now blink the forth number of the code.
Release the eject button and press it again.
The LEDs will go back to the 3 red flashing lights.

All four lights flashing - 0
One light flashing - 1
Two Lights flashing - 2
Three lights flashing - 3

It might not work.

Make sure your AV cables are plugged in correctly, if they are try a different set