Dolby Digital: Unless you are only planning to use the receiver with an audio-only stereo system, there's really know reason not to get at least a 5.1-capable unit. Even if you don't have a DVD player or another digital audio source, you'll be ready for them if you eventually do. Also, you usually get more A/V connections so you're less likely to run out of them.
Plenty of Inputs and Outputs: Count up all your devices you wish to connect and add at least one to that number. Having space to spare will save you from buying another receiver down the road. Be sure the inputs offer the best possible connections your equipment supports.
Multiple Digital Audio Connections: Not only do you want enough for all your digital devices (DVD player, digital cable or satellite receiver or gaming system), you'll want to be sure you have both types. Digital audio connections come in two flavors: Toslink (the little square connector) and Coaxial (similar to an RCA-type cable, but usally thicker - and orange) are two types that equipment uses. You'll want both. You may want to look for a digital audio output, as well for recording to a digital device.
Assignable Audio Inputs: Since you don't need certain audio connections for some devices, you want to make the most of the better ones. Some receivers allow you to choose which video connections will get which audio inputs. This way, you won't need to waste a digital audio connection on your analog VCR.
Front Inputs: This makes it easier to connect devices like camcorders that you often unplug. With a set of front inputs, you won't have to fumble around in back of the receiver.
Test Tone: Though it's less of a tone than a hissing sound on most receivers, the test tone allows you to properly set up your speaker levels. Since every room is different, you need to adjust the sound output of the various speakers so they produce sound at the proper levels for your environment.
LED or LCD readout: This eliminates a lot of guessing when switching between sources or adjusting settings. The best readouts have easy to read displays that can be seen from across the room. Many have the ability to dim after a certain amount of time so they don't distract from your entertainment.
Rotary Volume Control: A rotary volume control makes it a bit easier to adjust the volume than a push-button control. It also tends to remember your volume level when the unit is turned off or unplugged.