A rumor was a statement, true or untrue, that was gossiped or speculated about.
According to T'Pol, as of 2152, the Romulans were rumored to be an "aggressive, territorial species". (ENT: "Minefield")
In 2259, Captain Marie Batel noted to Captain Christopher Pike that she kept hearing rumors that the Romulans were developing new weapons, but Pike was dismissive as he considered Romulans to be the boogeymen. (SNW: "A Quality of Mercy")
In 2267, when James T. Kirk professed his innocence in Benjamin Finney's untimely death to Areel Shaw, she told him that wasn't what rumors indicated. (TOS: "Court Martial")
In 2364, William T. Riker noted that everything the Federation knew about the Romulans up to that point had been based on rumor or conjecture, (TNG: "The Neutral Zone")
As of 2368, Riker had heard rumors about The Children of Tama for years. (TNG: "Darmok")
In 2370, Kalita informed Ro Laren of a disturbing rumor she'd heard from a trader on Pendi II; namely, that the Cardassians were going to supply colonists with biogenic weapons. (TNG: "Preemptive Strike")
As of 2375, Son'a starships were rumored to have isolytic weapons. (Star Trek: Insurrection)