I was quite surprised when I learnt that a maximum likelihood estimate follows asymptotically a normal distribution with the mean being the estimated value and the variance being the inverse of the Fisher Information multiplied by the number of observations.
Asymptotically means when you have a big number of samples to calculate your ML estimate.
This is quite a remarkable fact. Some information:
http://math.arizona.edu/~jwatkins/o-mle.pdf (page 10)