Deafness

Mumps

Reports of sensorineural deafness after measles, mumps, and rubella immunization. 1993, Stewart, Arch Dis Child

Here is the description of 9 cases of deafness after the MMR vaccine within four years of vaccination. The authors conclude that in 3 cases deafness was unrelated to the vaccine (but they do not provide an explanation for this conclusion), and in 6 other cases it may or may not have been related to the vaccine.
Since unilateral deafness is hard to diagnose in children, and they get vaccinated at the age of 12 months, there may have been other cases that were missed.
The authors suggest checking children’s hearing upon admission to school and comparing it to historical data, in order to understand whether the MMR vaccine affects hearing.
Another 44 cases are described here.
A few more cases of deafness after the MMR vaccine: [1], [2], [3], [4], [5], [6], [7], [8], [9], [10].