Almost all passports I have seen have a place of birth field on them. For instance, on the US Passport,
Is there a specific reason to this?
An immediate reason is that some international norms recommend it but they do not mandate it (the ICAO coordinates this at an international level, see comments for more detail). EU passports must also mention it. A more general reason for ID of any kind to have a date of birth and place of birth is to be able to distinguish people with the same name (Wikipedia has more details on this).
But possibly the most important reason is that in many countries, your place of birth would also have a register that would include a note of your birth and, eventually, of your death so you can always come back to that register to verify that someone is not trying to use a made-up identity or a dead's person identity. Before computer databases, it was the main mechanism to maintain and access this information.
Incidentally, I believe the Swiss passport does not have a “place of birth” but a “place of origin” (Heimatort or Lieu d'origine), which is the place your family comes from and can be transmitted from one generation to the next even if you never lived there.
It's not the happiest of reasons, but quite a few countries care not just what your country of citizenship is, but where you or your family is originally from. For example, India imposes additional restrictions on anybody of Pakistani origin, anybody born in the ex-USSR must prove they have renounced their citizenship if applying for a Russian visa, people born in Israel may face unwanted extra attention in much of the Middle East, a friend of mine whose birth certificate calls him "Mohammed" with place of birth "Baghdad" had significant trouble getting a US visa even though he's lived in Israel as "Herzl" since age 5 and is more Jewish than a bagel, etc etc. And the "place of birth" field in the passport makes it very easy for these countries to see where the applicant is from.
I think just the fact that it's one of the few attributes of a person that is generally verifiable (through birth records), and will never change, makes it useful to include on a passport or other document of identity.
You can change your country of citizenship, your name, and even your sex, but the circumstances of your birth will never change.