Yes, your Xbox 360 has some value in today's market, though the exact amount depends on several factors23. These include the model, condition, whether it's complete with original packaging, and if it's a special edition23.
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An Xbox 360 in full working order will be worth more than one that doesn't turn on23.
A complete Xbox 360 with the console, controller, and proper packaging will be worth more than a loose unit2.
Keeping the original cardboard packaging can increase the value2.
Limited edition models, such as the Halo Special Edition or Mountain Dew Xbox, can fetch higher prices2.
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A loose Xbox 360 console (no box or accessories) can sell for $40 to $90, depending on its condition2.
A complete original Xbox, with the console and a controller in the proper packaging, typically sells for $140 to $1902.
GameStop offers up to $37.40 in store credit or $26.18 cash for a Microsoft Xbox 360 S Console 4GB - Black Pro Value7.
It's worth noting that the Xbox 360 is at a good stage now, not old enough to be considered retro but still desirable1. Physical media is still readily available, and many games don't require installation to a hard drive1. Selling games separately, like Guitar Hero Metallica, might also increase profits4.