For declarative, where you describe what you want, not how to get it, you have Prolog, Make and SQL (maybe others but I haven't heard of them). Yes, they technically aren't purely declarative as they usually have an escape hatch to imperative for performance reasons, but you can get quite far with them just in a declarative style.
The imperative, where you tell the computer how to do something, you have procedural (Pascal, Ada, C, BASIC, Cobol, Fortran) that's your classical programming style of actions working on data. There's object oriented (Smalltalk, Java, Erlang) which structures things a bit differently than procedural, where data is told what to do (via methods or message passing). Functional languages are more about avoiding globals and controlling side effects (and typically are lazily evaluated, but I don't think that's foundational to functional). You have concatenative (Forth, Postscript, Joy) which centers around a point-free style of programming (implicit data on the stack instead of explicit in variables) and data-flow (or array-centric) languages (APL, J, K) which work natively on array data.
Each of these paradigms have their pros and cons. Procedural if you have a lot of actions on a small set of types. Object oriented if you have a lot of types and a small set of actions. Functional if you want easy-to-reason about code. Data-flow to help with parallelism. Concatenative if you don't want to name piece of data. Declarative to have the computer figure things out for you. All of these I can see a reason to use in production.