The evidence is very mixed. Wearing a helmet does significantly reduce the risk of head injury in a crash, but riders who wear helmets appear to be at significantly higher risk of crashing. This may simply be selection bias (frequent cyclists engaged in risky types of riding are more likely to wear helmets) or it may represent risk-compensation by cyclists or other road users.

http://www.cyclehelmets.org/1052.html

The evidence is clear: https://helmets.org/stats.htm

This is for the US, the country that appears to be almost fanatically opposed to making safe cycling paths. Of course you're going to have more terrible accidents then (with or without a helmet).

Perhaps people who wear helmets are generally more careful so there are less severe accidents - still : impressive numbers