Adenoviruses, of which there are over 40 different "serotypes" in humans, are responsible for 5-10% of upper respiratory infections in children, and many infections in adults as well.
Most infections with adenovirus result in infections of the upper respiratory tract. Adenovirus infections often show up as conjunctivitis, tonsilitis (which may look exactly like strep throat and cannot be distinguished from strep except by throat culture), an ear infection, or croup. Adenoviruses can also cause gastroenteritis (stomach flu). A combination of conjunctivitis and tonsilitis is particularly common with adenovirus infections. Some children (especially small ones) can develop adenovirus bronchiolitis or pneumonia, both of which can be severe. In babies, adenoviruses can also cause coughing fits that look almost exactly like whooping cough. Adenoviruses can also cause viral meningitis or encephalitis. Rarely, adenovirus can cause cystitis (inflammation of the urinary bladder -- a form of urinary tract infection -- with blood in the urine.
Most people recover from adenovirus infections by themselves, but people with immune-system problems sometimes die of adenovirus infections, and -- very rarely -- even previously healthy people can die of these infections.
Adenoviruses are often transmitted by coughed-out droplets, but can also be transmitted by contact with an infected person, or by virus particles left on objects such as towels and faucet handles. Some people with adenovirus gastroenteritis may shed the virus in their stools for months after getting over the symptoms. The virus can even be passed from one person to another through water in swimming pools that do not have enough chlorine in them. As with many other illnesses, good handwashing is one way to lessen the spread of adenoviruses from one person to another. Heat and bleach will kill adenovirus on objects.
As with most viruses, there are no antibiotics that help with an adenoviral infection, so treatment is largely directed at the symptoms (such as Tylenol® for fever). I will often give antibiotic eyedrops for conjunctivitis, since it takes a while to test to see if the eye infection is bacterial or viral and to help prevent bacterial "superinfection" in cases of viral conjunctivitis. If I see tonsilitis, however, I will always check (first with a rapid test for strep, then with a throat culture if the rapid test shows no strep) for bacterial infection before treating with antibiotics, to make sure that the antibiotics are truly needed.
In the past, US military recruits were vaccinated against two serotypes of adenotypes, with a corresponding decrease in illnesses caused by those serotypes. The vaccine is no longer manufactured, and there are currently no vaccines available to protect against adenovirus. Good hygiene, including handwashing, is still the best way to avoid picking up adenovirus from an infected person.