OS X Xbox 360 to iMac 27 inch.

nope

There's no way to do that, unfortunately. Maybe on Apple Display but it hasn't got hdmi or you're gonna convert hdmi to dp which is unnecessary to work on it.

There is an adapter that was sold for the 27" iMac. It wasn't cheap and it only supports 720p.

http://tinyurl.com/c55xqzl

RocYourSox said:

Is there a way to use my Xbox 360 on my iMac? If so, what cables do I need?

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depends, if you have a mac with a thunderbolt port, no. but if you have a mac with a minidisplayport, yes.

cosmicjoke said:

depends, if you have a mac with a thunderbolt port, no. but if you have a mac with a minidisplayport, yes.

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you can use thunderbolt as mini display port. that's not the point. maybe there is a application for that.

I have not done this personally, but this looks to be relevant:

http://macs.about.com/od/usingyourmac/qt/using-target-display-mode.htm

ActionableMango said:

I have not done this personally, but this looks to be relevant:

http://macs.about.com/od/usingyourmac/qt/using-target-display-mode.htm

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That does not apply to Thunderbolt iMacs