Does the receiver have all the connections you need? As mentioned above, most modern electronics rely on HDMI cables to transfer audio/visual signals, but many devices -- particularly older ones -- use alternative connections, such as optical or coaxial digital audio; components or composite video; and analog (stereo or multichannel) audio. Take stock of your home theater and make sure that whichever receiver you buy can support your personal collection of electronics. If you have several HDMI devices, make sure the receiver has enough HDMI connections for your needs.
Make sure it fits! Some of the more expensive receivers available are very bulky. Before you buy, measure your entertainment center to ensure the receiver you want can fit in its future home.
What features do you want? Oftentimes, the difference between two competing receivers lies solely in their feature set. Almost all home theater receivers support 3D Blu-ray and HDMI's audio return channel functionality, but various receivers include various Internet-enabled apps, wireless networking, an iPod dock, AirPlay support, automatic speaker calibration functions and more.
Seven-channel receivers add flexibility. All seven channel receivers let you add two rear-center channels. Some (those equipped with Dolby Pro Logic IIz) let you use those channels instead to drive front-channel height or (in those receivers equipped with Audyssey DSX) front-channel wide speakers for a more immersive five-channel surround-sound field. But, before you decide that seven-channel sound of some type is a must, take stock of your listening room -- and how else it is being used -- to see if setting up seven speakers is practical or aesthetically desirable.
Check the manufacturer's policy before buying online. Some manufacturers have strict policies regarding authorized dealers. Denon, for example, clearly warns prospective buyers that their warranty is not valid if they don't purchase their receiver from an authorized retailer or if the serial number has been removed or replaced to prevent tracing the receiver's original source. Some retailers offer their own warranties in such cases, but the decision on whether that's sufficient is one that should be carefully weighed.