The Time Lords' First Law of Time set out to prevent anachronisms such as a person meeting other versions of themselves (TV: The Three Doctors) or returning Eldrad to her present, by that time (from a 20th century point of view) the distant past. (TV: The Hand of Fear)
Examples of their creation
The Monk had, by the time he met the First Doctor in 1066, caused many deliberate anachronisms in Earth history to "improve" it. (TV: The Time Meddler) The Fourth Doctor caused anachronisms of his own by deliberately defacing copies of the Mona Lisa, writing with felt tip pen on the canvas, "This is a fake". The words were readable in the 20th century after X-rays had been discovered. (TV: City of Death)
Upon seeing a Sontaran teleport pod in the Rattigan Academy, the Tenth Doctor told Luke Rattigan that "it might be Earth technology, but that's like finding a mobile phone in the Middle Ages", pointing out that the presence of such futuristic technology was an anachronism. (TV: The Sontaran Stratagem)
Spending three weeks in 1138 Essex, the Twelfth Doctor entered an axe battle playing an electric guitar solo while riding a tank, and introduced its citizens to the word "Dude" several centuries too early. Missy had ironically told Clara Oswald to keep her eyes open for the slightest anachronisms prior to the Doctor's entrance. When Colony Sarff arrived, he threw a heavily weather beaten sonic screwdriver at the Doctor's feet; after he, Clara, and Missy were taken to be brought to Skaro, the screwdriver, tank, and guitar were all left behind. (TV: The Magician's Apprentice)
Examples of their prevention
Both Rose Tyler (TV: The Unquiet Dead, PROSE: The Clockwise Man) and Jack Harkness (TV: The Empty Child) made it a point to dress appropriately for the time period they were in; much to their ire, the Ninth Doctor opted to change his shirt rather than his conspicuous leather jacket.
Since portable stereos did not exist in the 1960s, the Seventh Doctor called the tape deck that Ace carried around with her in Shoreditch in November 1963 a "dangerous anachronism." (TV: Remembrance of the Daleks)