Just a quick word about the online part of Demons' Souls:
In online mode, you get a few main things in addition to the offline game.
1) You can find other player's bloodstains and touch them to watch a phantom replay the last moments before their death. Occasionally, this may be useful to warn you of something. Like if you see the phantom run ahead and get killed at a blind corner, you might want to be on your toes as you approach it, etc.
2) Players can leave messages that can be read by anyone else online. These messages are written by choosing from preset parts, but the range of what you can say is quite large. You can leave (and read) warnings, advice on how to handle enemies, directions for avoiding traps or finding items, etc. The messages left there will stay a certain amount of time, but eventually fade away.
3) When other online players are in the same area you are, you can sometimes see white phantom characters. This is basically you watching what the other online player is doing in real time, though there is no way that you can interact with a white phantom.
4) Players in Body Form have the option to summon up to two other online players into their game as helper "blue phantoms". The blue phantoms can aid the summoning player, but the level progress made stays with the summoner's game. IIRC, the blue phantoms can get their Body Form back if they help the summoner defeat a level boss.
5) Players in Soul Form have the option to invade the game of a Body Form player as a "red phantom". The red phantom players then travel through the level that the Body Form player is in, trying to kill him. This is where the PVP (Player Vs. Player) aspect of Demons' Souls comes in, and there has been a lot written about build advice and strategies for excelling in PVP. There is also a way for two players to enter an arena for pure PVP duels.
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All that said, the biggest things that would be lost from the lack of online play are the PVP and blue phantom parts. These can be a really fun part of the game. But as far as the core Demons' Souls experience goes, the rest is nice but not necessary. The white phantoms, online bloodstains, and messages are all a nice touch, and can be helpful at times, but they can be useless just as often. Not really a make or break thing. And if you are trying to manipulate World Tendency or Character Tendency, it can be much easier doing so offline, since in online mode your WT is synced to the server WT. Those who haven't played the game don't need to know what WT and CT are just yet; only know that you will have to alter them if you want to get certain weapons, armor, items, etc. It is easy to change them in offline mode, but the server sync can mess you up in online mode.
Long story short, significant side parts of DS would be lost if the server goes down, but the core game would not be tarnished from a lack of online play.
