You could say: It was raining cats and dogs. I hear a lot of American use this slang, It is very common slang :)

You can also say "heavy rain". For example: It has been raining heavily all afternoon.

Usually we say "it is raining hard" or "it was a hard rain." It means that it rained a lot.

You might be interested in singer Bob Dylan's famous song, "A Hard Rain's a-Gonna Fall." Like many song lyrics it is not strictly correct good English, but it does illustrate the phrase "hard rain." Wikipedia, http://en.wikipedia.org/wiki/A_Hard_Rain's_a-Gonna_Fall Lyrics, http://www.bobdylan.com/us/songs/hard-rains-gonna-fall Youtube, http://www.youtube.com/watch?v=-ex-m-eEKsg

You have to be careful though, consider this question and 2 different responses: Q: What's the weather like out? A1: It is raining hard out there. A2: It is hardly raining out there. Those two answers actually mean completely opposite things. A1 means there is a lot of rain falling. A2 means it is not raining very much out.