The generic term for these devices, at least in the UK is tv card. They come in internal, eg. PCI and external, eg. USB forms and can accept different types of input, eg. dvb-t, dvb-s, analogue.
My own selection (all of which work on Linux but with levels of effort required ranging from none to compiling V4l drivers are:
HVR 1100 and the 1110 Hauppauge package as an 1100 (the latter needs a firmware download but otherwise works out of the box on later linux and uses different chips - the differences are no odds to Win users who have relevant drivers supplied in the box but that type of thing can be the difference between success or failure for a Linux user,). Nova-T 500 again works out of the box with firmware. Cynergy XS (needs V4L drivers built + firmware for me).
Jon (who again finds a post fails with a name in the From box)