Short answer No if travelling in France Spain Italy or on Eurostar. 

Not on a train that requires mandatory reservation.

What train/s are you thinking about?

In Sweden you also need reservations on high speed trains and also on intercity trains.

Many high speed, long distance and cross border trains require IR pass holders to have a reservation. If you board one of these without a reservation there is a likelihood that you will either have to buy an in travel reservation or even a full ticket (with a penaltyfor not having a valid ticket) or even ejected from the train at the next stop.

In the main reservations are simple - either pre-buy from one of the on-line several agencies (including the IR reservation tool) or if you want a flexible trip simply go to the ticket office and buy before boarding.

Although Eurostar and French TGVs do have limited seats for IR pass holders, for October you can already check availability for many of these.

Oh sorry, i am talking about italy. I will book seat reservations spontaneous, because i dont know yet when i will travel and where i am going to. 

Most of these trains have gates which you can only pass with the code from the RES-even in some stazione grande in IT.

That is the spirit of Interrailing - just be philosophical. Italian railways (Trenitalia) are widespread and frequent. They are rarely over full so you will be fine.