So, it happens. Your train gets delayed and you miss a connection. Not to worry though, you are covered by laws! The official website by the European Union has a handy tool and the actual legal text. In short: you have right to delay compensation of at least 25% of a single ticket if between 60 and 119 minutes late, or 50% of single ticket if more than 120 minutes late. As Interrail/Eurail values a single incident (more on this later) at €48 this means you’ll get €12 or €24, to a maximum of 50% of your total pass value.
Another great resource is Jon Worth’s diagram to compensation, which is a bit more general than just for Interrail/Eurail.

Rules

Your Interrail/Eurail ticket counts as a single ticket for these purposes, EXCEPT if it is a mandatory reservation train. These count as their own tickets and thus through delay compensation is not available. The exception to this exception is if your non reservation compulsory train is operated by the same company as your compulsory reservation train. You can claim multiple delays on one day, as long as you stayed for at least 2 hours somewhere in between (as tried and tested by a writer of this wiki).

Furthermore, claims are not just for the €12 or €24 compensation, but also for costs such as a hotel night, paying for your own transport like a bus or ferry (but not a plane or taxi) if after 100 minutes after the original departure time you still haven’t gotten an alternative/hotel from the train company, and food costs if this was necessary due to unforeseen stays in places for example. Before booking things yourself it is required to contact the railway company that made you miss your connection/cancelled/delayed your train, as they have the authority to issue hotel vouchers, so you don’t have to spend a lot of money on a last minute hotel.

To request compensation from Interrail/Eurail make sure you keep all receipts from additional purchases, and contact customer support/the train company for assistance before booking things yourself. Also make sure you get proof of delay as it can be hard to get this online occasionally!

A little extra

If you’ve travelled by high speed rail in (mostly western) Europe you may have seen the term HOTNAT (Hop On The Next Available Train). This is a cooperation between the Railteam alliance, which they do voluntarily but agreed upon in writing, as visible on their website. This is only applicable to high speed trains by the operators. This can be very useful if you miss an Eurostar to London because the ICE from Germany was late at Brussels, or vice versa!

Links

Requesting compensation for Interrail can be done here: https://www.interrail.eu/en/support/delay-compensation
For Eurail you can use this form: https://www.eurail.com/en/help/delay-compensation