Bluing/black oxide is the most common finish. It can be very attractive, but probably offers the least rust resistance. There's actually quite a few different types of bluing.
Parkerizing is a moderately common finish. It is a porous finish, so it will soak up oil and can offer excellent rust resistance. I've found it to be a little soft, though, although it can vary a lot in durability.
Anodizing- for firearm use, only aluminum (and occasionally titanium) are anodized. They can't be blued or parkerized. Aluminum is almost always anodized. Hard anodizing (or type iii) is generally considered the best for firearm use.
Cerakote is expensive paint. I don't have any particular experience with it.
For some reason, nickel boron is generally only applied to AR15 BCG's. I'm not really familiar with it.
Nitrocarburizing is more of a surface hardening process than a finish. Usually, a black oxide finish of some kind is applied over it.
Not covered-
Stainless steel- it's the composition of the metal rather than a finish. It's stainless all the way through. It offers excellent rust resistance, although it can rust if abused. Since it is stainless all the way through, it can be readily refinished.
Nickel- electrolytic nickel is more of an old timey finish and can have issues. Electroless nickel can be almost as good as hard chrome.
Hard chrome is likely the most durable finish of all, but many find the bright silvery appearance offensive.
