Demon's Souls is my favorite by a hair, with Bloodborne coming in behind it.
The reason Demon's Souls is my favorite, though, it because of one simple stupid fact: summoned allies are blue, and they don't have to be cops to do so.
Other reasons include a respect for how well it plays, the MP system, the slightly more coherent (yet still implausibly incoherent) story, and the final boss.
This is a game from 2009. Playing it again recently (to finally Platinum it and complete my journey in said game) has revealed one amazing fact: This game hits 40FPS almost all of the time and looks just as good as Dark Souls 1&2. This is an impressive feat, especially considering the next PS3 Souls game, DkS1, stuttered the entire game.
And MP. If I want to be a mage, I don't want to worry about filling slots up with the same spell over and over so that I don' run out before I reach the boss. I want to equip an MP regen item and as many varied spells as I can. Demon's Souls (and now supposedly Dark Souls 3) will allow that as well, so yay.
And then there's the story. Sure, you still have no idea what's going on. But instead of telling you "You're undead, now shoo and go do something grand", the game gives you a rundown on the history of Boletaria (twice). Does this explain who the Old Monk is? No. Do you have any idea who he is? Not a clue. But you at least know exactly what will happen once he's dead.
And poor, poor King Allant. All of that power you thought you were going to get, and here you are. A pathetic, disgusting waste of goopy flesh(?). You die in 4 hits, and your excuse for retaliation looked more like a dying animation than an actual attack. You weren't difficult at all, but it was still hard to kill you. It was like murdering an elderly man who had fallen over. I love that the final boss of such a hard game is almost nothing, and the lesson that it teaches the player is a good one. If you seek power, it may leave you weaker than before.
Overall, Demon's is also probably the most different in general design than the rest of the Souls games. Where DkS1&2 and Bloodborne are both open-ended 3D Metroidvanias, Demon's is more of a 3D Megaman. Pick your level, wreck or get wrecked by that level, move on to the next area of that level. OR you can go try a different area and beat that area's first boss, too. In this way, Demon's has the most open ended way to play the game: Maybe you want to knock out the Valley of Defilement first and foremost, because you didn't cry enough last time you fought Astraea. Fine. Maybe you want to take the easy route like I mentioned before by fighting all of the first bosses, than the second, then the third. This is actually kind of what the game wants you to do, as the final boss (in terms of definition, not who is actually the last enemies with a health bar) is actually the fourth boss of the first area. Either way, every zone in the game is opened up to the player from nearly the very beginning. As soon as the player beats the first boss in the game (Phallanx), the rest of the Archstones open up and the Maiden in Black tells you to git gud.
So for me, Demon's is the best. I can only hope that they remaster is for PS4 and add in that lost area (there were originally 6 Archstones, but the Land of Giants was cut due to time constraints and was to be added in as DLC, but never was). Demon's Souls released in 2009 exclusively on PS3.