When one says "classification" in math, usually one of a handful of examples springs to mind:

-Classification of Finite Simple Groups with 18 infinite families and 26 sporadic examples (assuming one believes the Classification is indeed complete)

-Classification of finte-dimensional semisimple Lie algebras with 4 infinite families and 5 exceptional examples

-Classification of (Simple, Formally Real) Jordan Algebras with 4 infinite families and 1 exceptional example

I'm sure there are other examples that non-algebraists would think of before these. All the examples I cited take the basic form of having several infinite families and some number of exceptional examples which do not fall into any of these families. Thus I am wondering:

Question:Does anyone know of examples of classifications of some mathematical objects such that the classification consists (A) only of infinite families or (B) only of a finite number of examples/ an infinite number of examples which do not seem to be closely related to one another (i.e. they do not "appear" to form any infinite families).

One example of case (B) that comes to mind would be finite dimensional division algebras over $\mathbb{R}$ of which there are 4. On the other hand, for case (B) I would like to rule out way too specific "classifications" such as "finite simple groups with an involution centralizer of such and such a form" since this is really a subclassification within the classification of FSG's. Although I am an algebraist, I would like to hear about examples from any branch of math, for comparison's sake.

(If anyone thinks of better tags for this, feel free to add or suggest them).