These pages expand on Robert's answer with some interesting examples:

http://www.kentlaw.edu/academics/lrw/grinker/LwtaThat_Versus_Which.htm http://www.kentlaw.edu/academics/lrw/grinker/LwtaClauses__Restrictive_and_Nonrest.htm

I'm not sure where I picked this up or if I made it up, but here's a basic rule about this that is fairly solid: It's always that, unless you mean which.

Clauses beginning with "which" should be offset by commas. For a non-restrictive clause to be non-restrictive, it becomes, essentially by definition, parenthetical. The most common error in word choice is definitely the overuse of "which." Because proper "which clauses" are more difficult to create, let's consider one that is correctly formed.

Incorrect: This rule that I find absurd should not be followed exactly by anyone.
Correct: This rule, which I find absurd, should not be followed exactly by anyone.

The core sentence is "This rule should not be followed." The parenthetical remark can be removed without any loss of meaning, clarity, or force. The notion that I find it absurd is non-restrictive. Whether I do or not, "this rule" should not be followed.

Now, is it possible to add context such that this same clause could justifiably be considered restrictive, instead of non-restrictive? Yes. Take for example this:

Absurdity is something few of us can tolerate, and of the things that we have become habituated to tolerate, we should stop to consider every once in a while if we should not make an effort to draw the line here and now, and put an end to it if possible. Rule XYZPDQ is an absurd rule for reasons A, B, C, and D, which I have enumerated elsewhere. We have tolerated it in the past, but now I say no longer! This rule that I find absurd should not be followed exactly by anyone.

As hopefully it is plain to see, the context of the paragraph creates a situation in which the notion of absurdity is the very point of the rule that is being called into focus and, therefore, takes on a restrictive quality--to the point that using which in this case would actually be incorrect.

The context of the source example is actually somewhat ambiguous. The whole sense of the source statement is basically:

Along with A-type registers, there are also B registers, C registers, D registers (namely D1, D2,...etc., which do X), and E registers.

There are two things about the basic rule that come into play: 1) whether "which" is correct or not does depend to some extent on the intention of the speaker, and 2) when using "which," you really should use a comma.

There are definitely some choices to make about how also to incorporate the information that is literally enclosed within parentheses along side the additional information in question.

Overall, what you notice stylistically is that the list provided does not conform to the ideal of parallel construction. It is only this one item that has additional detail, which tends to support the notion that the intention actually is parenthetical, thus perhaps justifying the use of "which." The lack of parallelism on its own, makes any solution somewhat awkward.

The bottom line is that if we infuse a content-aware knowledge of the greater context, this does indeed indicate that the meaning of the bulleted item actually is constrained by the detail of the added information and is, therefore, a restricted clause. (Again, this is not a purely grammatical issue, but depends on intention, which is part and parcel of the context.)

Ideally, the list would be filled out by creating a construction such as:

Along with A-type registers, there are also B registers that do Q, C registers that do R, D registers (namely D1, D2,...etc.) that do S, and E registers that do T.

Given that this is ultimately the proper solution for the larger trouble, and that when you create this solution it also clarifies the intention that the additional information for each item is clearly restrictive in the proper sense, I say that you would be on justifiable ground in changing the existing "which" to a "that".

I do agree that in formal writing restrictive clauses should always use "that." But the challenge of determining whether a clause is (or should be) restrictive is not always obvious (though most of the time it probably is). Conversely, for non-restrictive clauses, use "which" and signal that you have chosen purposefully by offsetting the remark with commas. And if adding a comma (or two) appears to have "changed your meaning," then that is a sure sign that you don't mean "which," and so should use "that" instead.

In your reference, the "use only 'that'" rule refers to restrictive clauses, where "which" is still used for nonrestrictive clauses. One guideline I've heard is that it's a nonrestrictive clause taking "which" if you can include "by the way" without changing the meaning.

Referring to a plural shouldn't affect the word choice. In your example, my (US English) inclination is to use "registers that determine", and "register that determines" also looks correct.