Yes, for the most part, dinner reservations are required. Especially on the weekends it is essential to have a reservation, otherwise it is almost impossible to get a table at any of fine restaurant in the city.
Fine dining restaurants like Ulus 29, Sunset, Mikla tend to be booked for most weekends. Mikla has two seatings, so it might be possible to get a table for second seating at last minute. However, most of the time, it's wise to call in the beginning of the week and sometimes even that is not early enough.
Among the traditional taverns, Karakoy Lokantasi tends to be booked, so if you have plans to eat there, it's wise to call a week in advance. In the winter, another popular traditional tavern, Asmali Cavit tends to be booked as well.
It also matters how big your group is. If you are a party of two, obviously you might get lucky and find a table in some of the nice restaurants. However, a party of six for instance, definitely must arrange the table at least a week prior to dinner date.
Afiyet olsun! (Buen apetit!)