Basically, I want to learn lots of programming languages to become a great programmer.  I know only a handful to depth and I was hoping someone could elaborate on how many classes or types of programming languages there are.  Like how you would lump them together if you had to learn them in groups.

Coming from a Java background, I'm familiar with static typing, but I know that in addition to dynamic typing there has to be such variety in available languages that I would love to see a categorical breakdown if possible.

It depends on how you want to classify languages. Fundamentally, languages can be broken down into two types: imperative languages in which you instruct the computer how to do a task, and declarative languages in which you tell the computer what to do. Declarative languages can further be broken down into functional languages, in which a program is constructed by composing functions, and logic programming languages, in which a program is constructed through a set of logical connections. Imperative languages read more like a list of steps for solving a problem, kind of like a recipe. Imperative languages include C, C++, and Java; functional languages include Haskell; logic programming languages include Prolog.

Imperative languages are sometimes broken into two subgroups: procedural languages like C, and object-oriented languages. Object-oriented languages are a bit orthogonal to the groupings, though, as there are object-oriented functional languages (OCaml and Scala being examples).

You can also group languages by typing: static and dynamic. Statically-typed languages are ones in which typing is checked (and usually enforced) prior to running the program (typically during a compile phase); dynamically-typed languages defer type checking to runtime. C, C++, and Java are statically-typed languages; Python, Ruby, JavaScript, and Objective-C are dynamically-typed languages. There are also untyped languages, which include the Forth programming language.

You can also group languages by their typing discipline: weak typing, which supports implicit type conversions, and strong typing, which prohibits implicit type conversions. The lines between the two are a bit blurry: according to some definitions, C is a weakly-typed languages, while others consider it to be strongly-typed. Typing discipline isn't really a useful way to group languages, anyway.
