The following will help you identify what version of XBOX you have.
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At this moment there are 8 main versions of Xbox.
The xbox v1.0 , v1.1, v1.2, v1.3, v1.4, v1.5, v1.6 and v1.6b.

It's possible to have an idea of the version you have based on the serial# ... but these checks are not (yet) 100% accurate.
If you want to really know what version you have you will have to open your xbox. If you want to put a modchip or flash TSOP in your xbox later you will have to open it anyway.

The Serial Number is located on a sticker on the back of the xbox underneith the MFG DATE.

Serial Number: XXXXXXX 20XXX = v1.0
Serial Number: XXXXXXX 21XXX = v1.0
Serial Number: XXXXXXX 23XXX = v1.0
Serial Number: XXXXXXX 24XXX = v1.1
Serial Number: XXXXXXX 25XXX = v1.1
Serial Number: XXXXXXX 30XXX = v1.2
Serial Number: XXXXXXX 31XXX = v1.3
Serial Number: XXXXXXX 32XXX = v1.3
Serial Number: XXXXXXX 33XXX = v1.4 or v1.5