Speed limits are older than the "horseless carriage" itself; the Locomotive Act of 1861 in the UK limited steam-powered "road locomotives" (train engines designed to travel on roads instead of tracks) to a maximum speed of 10 mph. In 1865 the speed limit was lowered to 4 mph and a requirement was added for a man carrying a red flag to walk at least 60 yards in front of the vehicle to warn others of its passage. In 1896, following the development of the modern automobile concept, the red flag requirement was dropped and the speed limit was amended to 8 to 16 mph at the local authority's discretion.

Two examples of roads I'm aware of which previously did not have speed limits, but on which they were introduced:

Speed limits were introduced on the UK's M1 motorway after racing driver Jack Sears tested an AC Cobra coupe at 185 mph on it in 1964, instigating a moral panic that led to the implementation of a "temporary" 70 mph speed limit in 1965, made permanent in 1970.

Numerical speed limits in Montana were implemented in 1998 after a man charged with speeding successfully argued before the state supreme court that the state's restriction to "reasonable and proper" speeds was unconstitutionally vague.