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Yes, you can.

There are lots of Freeview tuners out there.

For Freesat, without a Sky box, you can use one of these: http://www.avforums.com/forums/showthread.php?t=664704

Ever since I found that I've been intending to replace my Shuttle HTPC with a Mac Mini.

For Sky you'd still need a box for the viewing card- there are PC solutions for reading your Sky card. Personally I don't know of any Mac solutions for CF reading etc. You could get a USB tuner with general video inputs and connect the Sky box through Scart/AV cables though.
 
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