Yes, there is a similar regulation (EC) No 1371/2007 on rail passengers’ rights and obligations. Its application is mandatory for international trains operating within the EU. Member states may excempt domestic long distance traffic during a transition period. The regulation does not apply for domestic, regional traffic.
Summarized, it gives the passengers the right to
- a refund of 25% of the ticket price in case of a delay of 60 to 119 minutes at the destination station
- a refund of 50% of the ticket price in case of a delay of 120 minutes or more
- meals and refreshments within reasonable limits
- accommodation where a stay of one or more nights becomes necessary
- transport to the departure or arrival point if the train is blocked on the track
The refund must be made in cash, if the passenger requests so.
You can find a more complete layman-friendly summary of the regulations here.
Since international train travel in most cases involve several train operators, it may be difficult to find the right operator to contact for a refund. Usually, you can contact the operator, from which you bought your ticket.
It is perhaps also worth to notice, that some EU countries have national regulations and some train operators have their own refund conditions, which are more favourable for the passengers than this. E.g. in the UK, you can in most cases get a 50% refund in case of a 30 minutes delay and a 100% refund if your train is delayed more than one hour.