Aircraft cabins, to answer a commonly asked question, are probably about as clean as most other forms of public transport.
Aircraft are generally cleaned more rigorously when they stop for several hours, but cleaning crew on aircraft with a short turnaround have no time for anything more than a quick tidy-up. On a layover of several hours, tray tables may be wiped but they won't be disinfected, and using the same cloth to wipe from one to the next carries the possibility of dispersing bacteria more widely.
Although they might come wrapped in plastic, not all airlines launder blankets between every flight. The same goes for headphones, which might get a wipe-over but nothing like a complete sterilisation.
Another health risk comes from drinking aircraft tea and coffee. The water that is used to make these beverages typically comes from the aircraft's holding tanks. That's the same water that is used for washing in the bathrooms, which often carries the warning, "Not for drinking".
When the US Environmental Protection Agency sampled water tanks on American aircraft in 2004, one in seven tested positive for coliform bacteria. While these organisms are present in the human digestive system, their presence in drinking water comes with an increased risk of contracting a water-borne illness. The EPA subsequently launched initiatives to get airlines to clean their tanks but follow-up testing nine years later found coliform still present in one in every nine aircraft.
No tap water is completely sterile and a healthy immune system can handle some bacteria. Airplane coffee and tea are a low risk, but anyone with a compromised immune system should steer clear, and never give water from this source to an infant or young child.