Depends on the manufacturer, and if they offer TiVo style services with larger HDDs.
Sky+ for example, you can only swap the Maxtor HDD inside out with ones from the same production line (which vary from 20GB-160GB, but no longer as it's hardwired not to recognise anything beyond that)
Yet the V+ Box from Virgin Media you can swap any SATA-150 HDD in you want to... not that they made it easy getting in to the bloody thing using Triad bolts to seal it, searched for about 2 weeks to find the correct tool to open my box.
This said most of these Freeview/TiVo boxes will connect to Windows Media Center over a network, allowing you to record/view directly on your computer; might want to checkout if yours can do that before trying to swap out the HDD. Also know there are a few but forget (so might want to search for them) websites that provide information on compatible HDDs with varying devices.
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