If you want unique identifiers, use version 4 (random) UUIDs. Problem solved. The probability of a collision is roughly the same as the probability of a fully grown dinosaur spontaneously manifesting in your bedroom due to quantum fluctuations.
I will take my chance :-) More seriously, If you can use them, good old increments are probably best. They are fast and cheap. Especially in a database. They can have privacy/security issues (you could guess things by the values of ids of stuff). UUIDs are better in those case or when you deal with a distributed system.
Push them through a secure hash function, and that problem is solved too (assuming you can keep the base counter private).