Krist It depends. On some routes it is not necessary to book in advance, but on other routes the trains are fully booked in the peak times and now reservations are often mandatory, for example between Germany and other countries.
You can also save money. For example, a booking of a TGV in France costs 10 € in advance, 20 € to 40 € later. Unfortunately, it is not possible to reserve seats on the vending machines at the stations, you have to wait at the ticket office.