Well, I read a rather surprising post from Derek Lowe today. Turns out, he thinks that most common buffer reagents are a bunch of hocus-pocus:

There's some reducing agent in there, naturally. Can't have those thiols turning into disulfides and balling up the protein, I understand - but does something bad happen if it's not in there? Generally, no one finds out, because, hey, why mess with it? And there's some EDTA, and some salt, and their function is? Well, as far as I can tell, they're also in there because they've sort of always been. Same goes for the squirt of detergent (Brij-35 or some such), and the tiny bit of bovine serum albumin, of all things. It's just part of the old-fashioned recipe from Grandma's Protein Kitchen.

Now, organic chemistry has a little of this, true, but it hasn't reached quite the Ancient Runestone levels of enzymology.

Lowe unexpectedly sounds like so many of the physicists I know that make snap judgments about how biology is done without the requisite background. As it turns out, many people do understand each reagent's use and shortcomings. We use many of those reagents for reasons that we understand pretty well:

1. Reducing agents protect methionines and cysteines from oxidation. If the protein is an intra-cellular protein, then this mimics the reducing environment of the cell. If there are structurally or functionally important cysteines on the protein, this prevents them from forming intra- or inter-molecular disulfide bridges. Generally, one doesn't want those, because they can lead to the protein becoming insoluble. You may also need them if you're going to do mass spectrometry, because you want to know the molecular weight of the monomers (not the disulfide-linked Nmers). Plus there are multiple types of reducing agents, and there are situations where you'd use one and not the other.
2. EDTA is in there because the researcher wants to prevent magnesium or other divalent cations from somehow affecting the molecule of interest. This "somehow" can include metalloprotease degradation or bacterial growth. Sometimes you have your own reasons for not wanting a protein to bind Mg²⁺ (like if an enzyme gains a certain reactivity upon binding). Also, magnesium is required by some nucleases, so the addition of EDTA can also prevent nucleases from degrading DNA or RNA, if those are present in solution.
3. Salt is just silly to question. Most proteins depend on salt for stability and solubility. Salt helps screen attractive and repulsive ionic interactions.
4. Depending on the protein, you may require the presence of detergents to make the molecule soluble. There are many different types of detergents, and you'd choose one (believe it or not) rationally, depending on the type of interaction you want with the protein. There are cationic, anionic, zwitterionic detergents, and polar (but uncharged) detergents too. These are especially important for hydrophobic proteins that would otherwise aggregate were detergent not present.
5. BSA may sound silly, but it's a stabilizing adjuvant. Not only does it tend to keep the test tube feeling like the cell by acting as a crowding agent, it also acts as a sink for protease degradation in the case that some contaminant makes it in the tube accidentally. In our lab, we use it regularly as a blocking agent to prevent nonspecific protein-protein interactions and protein-surface interactions. I imagine Lowe would be shocked to also find out that we use α-casein from milk for the same purpose. The reason we use these animal-derived proteins are because of their cost; they are also abundant, have no relevant enzymatic activity, and work well.

Thankfully, Lowe doesn't question the actual buffer itself, which is probably the most critical ingredient because it stabilizes pH. There are dozens of commonly used buffers, each one optimized for particular chemistries and with different pK_a values. For example, you might need a buffer without primary amines that buffers well at pH 8, in which case you may pick triethanolamine over the more common tris.

Each of these ingredients—even if one doesn't understand how it works—is often a required buffer component. These reagents are the moral equivalent of the glass flask in chemistry. Sure, I could deride Derek for using such stone-aged materials as "super-heated sand" for his Erlenmeyer flask, or "baked mud" for his Büchner funnel, but that would be silly and take a rather healthy amount of hubris. Instead, I recognize that these are the basic tools of chemists, and we move on.

In much the same way, these buffer reagents are some of the most basic tools in biology; they combine to provide a tightly controlled and consistent chemical microenvironment for proteins and other macromolecules.