Some train types do require seat reservations while others allow you to just take any train with open seats. Sleepers/overnight, high-speed (e.g. TGV, Frecciaroso), long-distance and international trains always require seat reservations.
At peak times (e.g. Christmas or school holidays) it is strongly recommended that, wherever possible, you prebook seat reservations. Reservations can be prebooked through British TIPS with a seat reservation fee or you can purchase these in Europe, even on the day of travel.
REMEMBER: A pass allows you to travel on a train, but does not guarantee a seat on a specific train. If the train is full, you will need to wait for the next one.