Or are there scenarios where you don't want to add such a field?
Sure.
First of all, there are databases that have no autoincrements (e.g., Oracle, which certainly is not one of the smallest contenders around). This should be a first indication that not everybody likes or needs them.
More important, think about what the ID actually is - it is a primary key for your data. If you have a table with a different primary key, then you do not need an ID, and should not have one. For example, a table (EMPLOYEE_ID, MANAGER_IDTEAM_ID) (where each employee can be in several teams concurrently) has a clearly defined primary key consisting of those two IDs. Adding an autoincrement ID column, which is also be a primary key for this table, would make no sense at all. Now you are lugging 2 primary keys around, and the first word in "primary key" should give you a hint that you really should have only one.