I absolutely loved Heavy Rain! I consider it a huge improvement over Fahrenheit (aka Indigo Prophecy), although I still liked that game as well. I don't really agree with Jin about the game falling apart towards the end, I personally thought the game remained solid all the way through. The only real plot hole I can think of was explained in the deleted scenes which Quantic Dream released;
i.e. they had a paranormal explanation for something which happens in the game, but they decided to remove the paranormal aspect because they wanted to keep things realistic, which does make that plot point make no sense anymore (they should have just removed that plot point entirely instead of keeping it in with no given explanation).
Btw, as for gameplay; it's not so much a game as it is an interactive movie. Think point-and-click adventure game with the point-and-clicking replaced by button prompts. The gameplay is basically 80% QTE, except most of the time screwing up the button prompts won't get you killed. Oh, and the few times when your playable character can die, know that this game has 4 playable characters and if one of them gets killed, the story continues with the remaining characters. But you will always make it to the end of the game, it's not possible to get all 4 of your characters killed before the end of the game. I would recommend trying to keep everyone alive, though, unless you don't mind getting depressing bad endings (this game has a lot of different endings). There are at least 20 different ending scenes (emphasis on scenes, not endings; several endings share the same scenes).
As Jin said, there's also the spiritual sequel Beyond: Two Souls, but I personally felt that game was nowhere as good as Heavy Rain. The gameplay is pretty much the same, though. Except in Beyond you can't die at all, which made the game feel unrewarding to me. What's the point of getting the button prompts right if messing them up will never, ever get your character killed? There's no thrill during danger scenes because you know the main character can't die anyway.
PS: Heavy Rain can probably be considered a spiritual sequel to the previously mentioned Fahrenheit/Indigo Prophecy, which also has similar gameplay, but that one is considerably heavier on action scenes and your characters can very much die in that game, a lot more than in Heavy Rain (which is more forgiving in that regard). Fahrenheit is an old PS2 game, though, and I think it will be fairly hard to find (I had some trouble getting my hands on a copy of the game myself).
But yeah, Heavy Rain, Fahrenheit and Beyond: Two Souls are all plot-heavy games made by Quantic Dream.
Omikron: The Nomad Soul is their only game which is quite different (Omikron is a mix of Third Person Adventure/First Person Shooter action scenes/2D Fighter-style hand-to-hand combat and Open World exploration, quite a mix, eh? :happy5: ).