HDMI inputs are essential for a high-def television - it's the new format which combines digital audio and video in the one cable. HDMI is the best way to hook up a Blu-ray player, set top box or PVR to your television.
The HDMI inputs need to be HDCP-compatible (High-bandwidth Digital Content Protection) for watching commercial Blu-ray movies, but this should be standard these days.
You'll want at least two HDMI inputs on your television, and preferably one of them to have stereo audio inputs alongside it. This will give you the option of hooking up a computer via a DVI to HDMI cable and then running the audio over a separate 3.5mm to 2xRCA audio cable.
Many high-def televisions also feature a D-SUB PC input and stereo audio inputs for connecting a PC, although this may only support resolutions up to 720p.
Most televisions also feature composite and component video inputs, plus perhaps s-video and SCART. Extra inputs on the front or side of the television are handy if you'll regularly be plugging in a games console or camcorder.
A digital audio output (coaxial and/or optical) is handy if you want to connect the television to your surround sound system to listen to 5.1 sound from live broadcasts, although you're more likely to run the digital audio directly from your PVR and Blu-ray player to your surround sound amplifier.
Also in this series, How to Pick a Great Flat Screen TV, And Not Get Sucked In By Marketing Hype:
Part 4: LED and backlighting
Part 3: Screen size
Part 2: Refresh rates
Part 1: Brightness and contrast ratios
Also see our 5 tips for buying a digital TV set top box
And also see the lowdown on Freeview, and whether you should care
If you're new to Digital TV, or have yet to make the leap, start by reading Prepare yourself for Digital TV