I hear a constant hiss (or hum) from my speakers even with nothing playing. Should I worry?

Two different things, and the fix depends on which one you have. Hiss is the electronics' noise floor. Hum is electrical, and it deserves more attention.

Hiss first: a faint constant "shhh" from the tweeters, audible only with your ear near the speaker. Every amplifier has a noise floor and every tweeter reveals it. The test is simple. Inaudible from the seat: normal, ignore it, and stop putting your ear on the tweeter. Audible from the seat: something is adding to it. Check for a noisy source left connected and selected, gain set high on any external power amp (the AVR's pre-out then only needs a small signal and hiss rises with the gain), and enhancement modes that lift the top end. High-sensitivity speakers reveal more hiss by nature; a 92 dB pair will expose an amplifier a 86 dB pair would flatter.

Hum is a different animal: a 50 Hz drone, often louder with certain sources selected, sometimes with a buzz on top. That is a ground loop or interference, not the amplifier's noise floor. Unplug sources one at a time with the AVR on and listen; whichever removal silences it is the loop's entry point. Cable-TV lines and turntables are the classic offenders because they bring their own earth reference. Separate audio interconnects from power cables where they run parallel. Our subwoofer-hum answer covers the loop fix in more detail because subs are the most common victim.

The one case I would not shrug off: a sudden new hum with no wiring change. That deserves attention, and the list includes your home's earthing. A socket whose earth pin was never properly connected produces hum, and occasionally a tingle on the equipment's chassis, which is a safety issue rather than an audio one. See the power section for that. Hum that arrives with the monsoon and leaves in October is often the same earthing story told seasonally.

Tell us whether it is hiss or hum, whether it changes with source selection, and whether it is audible from the seat. Those three answers point at the fix.