theres a lot of kind of filters, like, low pass, high pass, pass band, and so on. also theres a passive and active filters. ohh yeah, and adaptive filters. just put in google "digital filters" or "analog filters" you can get your answer.
also you can be more specific in your question.
there are many more types of filters depending upon the network of electronics devices like resistors capacitors,configuration and most importantly approximations,in digital domain we've two main categories fir n iir filters