Flying some airlines such as KLM you can only choose seats for free while checking-in online on the day before. The economy seats in KLM's case are divided in normal, favourite, extra legroom and economy comfort.
I wonder, if all the normal economy seats are taken when I check-in, will I be able to choose seats in the three other categories?
Usually not. What will happen is that you will not get a seat assignment when you check in online and will be told to get the seat assignment at the gate.
At the gate, the gate agent will give you a seat vacated by:
a no show
a regular discount economy seat that is opened up by upgrading another customer to premium economy
Only rarely will you get a seat that was "hidden" from the customer visible seat assignment system. These will almost always be in your same class unless you have good mileage status with the airline.
If the airline has no spare seats by the time the doors need to close (and doesn't or can't upgrade economy passengers into a higher class), then the flight is overbooked and you may have to be "reaccommodated" on a later flight.
No, you will not be able to choose but you may get one.
Airlines block off some seats from online booking in order to accommodate travelers seating together. So there are most likely Economy seats available, even though you cannot see or select them. There is a possibility of overbooking, so in that case you will be given a seat of another type of possible of a different class, although this is increasingly rare.
The last possibility is that you may be given a seat in another flight! This will usually come with some form of compensation, not necessarily monetary, since it is the airline that chose to overbook. What you get depends on legislation and airline policy but Europe tends to be more generous with this type of compensation.
