A major failure on a transformer is defined as an incident that takes the transformer out of service for seven or more days. To determine the risk of unexpected failure, it's important to consider the consequences and the probability of failure occurring. About one out of every 200 transformers fails each year according to this CIGRE Transformer Reliability Survey. According to another study, major failures cost about $14,000 per MVA in property damage. It is safe to say that unexpected failure can be costly.
There are a lot of helpful resources to better understand what can fail on a transformer. It is important to evaluate the technical condition of the unit and the importance to the network, (aka the criticality), analysis of the make and model of the unit, unit features, years in service, location, and more when determining the risk. Transformer monitoring significantly decreases the risk of unexpected failure.