Simple answer: it depends on which tariff you have booked! In your order confirmation, under the fare conditions, you will find information about which piece of hold baggage or checked baggage is included in your booking.
If you want to travel without checked baggage, most airlines now have to book a larger piece of hand baggage. Unfortunately, the "classic small trolley" no longer counts as free hand luggage for many airlines.
Since the regulations change regularly, please check the exact dimensions of the piece of luggage on the respective airline's homepage before departure. Please note that the dimensions given always include the wheel and handles.
Here are the baggage regulations of the most common airlines:
Lufthansa/Swiss Air/Austrian Airlines