All reservations are not the same. There are seat reservation, for which national rail companies charge a few Euro (German Rail charges €4,50 for a second class seat, at the counter, about half online with a ticket purchase). For many trains, a seat reservation is mandatory, others just recommended.
What is referred to as a "reservation" for a night train is really a surcharge for the accommodations (cochette or sleeper), which is reserved for you. People without rail passes purchase a global ticket which includes use of the rails plus accommodations. Rail pass holders pay less for just accommodations, but passholder reservations are sometimes limited.
Many premium trains, such as Thalys, add a surcharge, called a "pass holder reservation", because they are more expensive to ride than the normal trains. All tickets come with a seat reservation, because all seats are reserved.
You absolutely should get a reservation for night trains, ASAP. I've seen night trains where everything except seats were sold out a month in advance. Often the most desirable accommodations are sold out several month in advance. Reserve these whenever you can commit. Some national rail companies (the Bahn) sell pass holder reservations online for trains in their country. Pass holder reservation for some country's trains are difficult to find, and you might end up going to RailEurope and overpaying.
Pass holder reservations for premium trains are limited. In busy times you want to reserve days in advance.
For regional trains, there are no reservations, required or made.
For the rest of the trains, reservations are probably not necessary, but are probably a good idea for longer trains. If you had to stand from Amsterdam to Milan, you would probably regret not spending €5 for a seat reservation. You should be able to get these reservations just before train time, certainly the day before. The only SRO train I was ever on had plenty of unreserved seats.