If you have watched the movie "Brazil" by Terry Gilliam then Ukraine will also be familiar. As a hang up from the Soviet times it still maintains an administrative system that demands paperwork – notarized copies and rubber stamps on everything – from buying an apartment to getting a refund because the battery is the wrong size for your torch.
The passport is the main personal document in Ukraine, needed for all official reasons. Any passerby may hypothetically be asked by a police officer to show their passport (and police use their right to check people looking for illegal immigrants but more often to fleece the tourist who has left his passport in the hotel room). Another example is that the Rail authority issues railway tickets with the name allocated in your passport - and these are checked against the passport data while boarding a train. So, it is recommended not to leave your ID document at home.
A driving licence or a local equivalent of SSN card (for example, in opposite for the US practise) have very particular, specialised, functionalities here. Ukrainians also have to get the foreign passports to go abroad.
Please look through the relevant sub-categories on the website or explore our Forum.