Perhaps the most important thing to investigate when shopping for an AV receiver is the number of connections it provides. Find out if there are enough for all the components in your current system, and that it leaves enough sockets free for future expansion. The more sockets it sports the better.
With so many devices offering high-definition pictures and digital audio over an HDMI connection, the number of HDMI inputs it provides is essential. The number typically ranges from three up to six or more. The other thing to consider is what type of HDMI inputs they are - if you already own or plan on investing in a 3D Blu-ray player and 3DTV then you have to ensure that your receiver has HDMI v1.4 inputs, which have the ability to accept 3D signals from the player and pass them onto the 3D TV. Thankfully most new receivers on the market feature HDMI v1.4 inputs, including many entry-level models, although it's not guaranteed.
If you're not going down the 3D route, then HDMI v1.3 inputs will suffice for all your other Blu-ray needs. This type of input is able to accept Dolby True HD and DTS HD Master Audio soundtracks as a digital bitstream, as well as multichannel PCM, and support other features like Deep Colour. You can also pass 2D high-definition pictures through these HDMI sockets, and some receivers can even upscale standard-definition pictures to 720p, 1080i or 1080p before sending them onto the TV.
Although most devices can output audio over HDMI, digital audio inputs may still come in handy for audio-only devices like CD players, older non-HDMI disc players and digital TV boxes. These come in two forms, optical (TOSLINK) or coaxial and they're usually accompanied by one or more outputs for passing the digital signal onto other devices like a recorder.
You'll also encounter a range of video inputs and outputs on the back of most receivers, including composite, component and S-video, allowing you to switch between various video sources at the same time as switching between audio sources. Their usefulness is diminishing as HDMI takes over as the de facto video connection for AV devices, but again you may still find them useful for older products.
What's more, some AV receivers can convert video signals fed into one type of video input and output them from a different type - for instance, you could connect a DVD player to the component video input but output the pictures to your TV over HDMI. This also saves you having to constantly change the input channel on your TV with several devices connected.