I've been playing computer games for about 30 years now, and RDR has grabbed me like few other games before it. Very few games would compel me to take time out of my day to write a post about it.
I don't like or dislike Western movies/games any more than the next guy, but they really nailed the atmosphere and setting. The game is beautiful. I've stopped to admire the vistas by starlight, and watched the sunrise from the porch of the general store while I waited for it to open. Riding through the wilderness in a thunderstorm, I was struck at just how wet and miserable everything looked. At atmosphere is great.
The writing and voice acting in the game is superb. Seriously, top notch. The writing is especially smart and poignant, and very engaging.
I really enjoyed both GTA:SA and GTA IV. I'm a big fan of the open world, where you can choose to follow the story line missions, or do side missions, or simply go out and explore. RDR has this in spades. It's so fun to load up your game and decide "what do I want to do today?" You always have a list of jobs to do, and they are all optional, so you can choose your own adventure. Hunting animals for skins (to sell for money), playing poker and other mini games, deciphering and following treasure maps, getting in shootouts with bandits, to say nothing of advancing the storyline by doing the set missions.
I haven't set foot in multiplayer yet, but I hear that is a lot of fun as well. I feel like I could go on and on. I'm completely smitten by this game.
A brief caveat is that there are some bugs. I've only seen one or two myself, but lots of people are reporting lots of issues.
If you've watched or read any reviews and the game sounds at all interesting, I can't recommend it enough.