The four main types of programming languages are:
1. Imperative Languages:
This language basically works on the sequence of operations that are performed by the computer. It focuses on how to get the exact result that is expected by the user.
Examples are C, C++, Java
2. Functional Languages
Lisp, Miranda, Gopher, Haskell. Bits of JavaScript
A functional language defines every program as 1 function.
3. Procedural Languages
These are the most well-known, like C, Pascal, C++, Basic, and Java.
All of these have multiple statements that are executed in order.
A subset of these are object-oriented, which means they work with classes and objects.
4. Declarative Languages
SQL is the most obvious example. Or Prolog.
In these, you define the output you wish to receive, and an internal 'engine' figures out how this can be achieved best. These languages are less general purpose, but very powerful in their field.
In any of these languages, you can use dynamic or static typing, and it can be either interpreted or compiled.