A systems language, like C, C++.
A managed language, like Java, C#.
A weakly typed language, like Python, Lua.
A web-server centric language, like PHP, Ruby.
An automation language, like Bash, Batch.
A functional language, like Erlang, Haskell.
A domain-specific language, like SQL, Mathematica.
[edit]This is a good 8th category:
And if you want a 9th, try a logic language, like Prolog.In my opinion add an Assembler Language and the list is complete