Missables in Demon's Souls

There a few missable items in Demon's Souls.

The first, as pointed out by Jim Bolia, is that worlds have different tendencies, white and black. This determines the difficulty of enemies, souls dropped, et cetera. At Pure White World or Pure Black world tendency, however, the maps themselves sometimes change. New paths may open up, or an additional (unique) enemy may spawn. World Tendency is effected by a variety of factors, such as beating a boss, dying, defeating certain enemies, et cetera.

See below for more details on what you find at each, and how the system works. Effects of:

White World Tendency

White World Tendency has the following effects.

Decreases enemy HP, attack and defence power
Enemies drop fewer upgrade stones
Enemies drop more healing items.
Attack power is increased in Soul Form. Increases 10% at White, and 20% at Pure White. 

See the list of White World Tendency Events. Black World Tendency

Black World Tendency has the following effects.

Increases enemy HP, attack and defence power
Enemies hold more Souls
Enemies are more likely to drop rare items
The Black Phantoms versions of enemies and NPCs appear in specific locations 
Black Phantom versions of normal monsters have a 100% drop rate
for their primary items.
Primeval Demons appear in specific locations in each world. Note that
Primeval Demons will appear slightly
before a world is Pure Black, so this
is not a good way to judge if you have
achieved Pure Black World Tendency.
This demon will still be there when
 the world is Pure Black.
Your character's maximum HP in Soul Form is reduced.

See the list of Black World Tendency Events.

Changing it:

Changing World Tendency

Nomenclature

Each action below is followed by a positive or negative number.

Positive numbers shift the World Tendency towards White (e.g. +1 means

one step towards Pure White World Tendency) Negative numbers shift the World Tendency towards Black (e.g. -1 means one step towards Pure Black World Tendency)

Towards White

Kill a Demon (boss) in a particular World (+1)  
Kill the Red Dragon (+1) in 1-2  
Kill the Blue Dragon (+1) in 1-4  
Kill the Black Phantom Form of one of the 5 special named NPCs that
appear in Pure Black World Tendency  
    Defeat Black Phantom Executioner Miralda (+3) in 1-1  
    Defeat Black Phantom Scirvir, the Wanderer (+3) in 2-2  
    Defeat Black Phantom Lord Rydell (+3) in 3-1  
    Defeat Black Phantom Satsuki (+3) in 4-1  
    Defeat Black Phantom Selen Vinland (+3) in 5-2  
Defeat a Primeval Demon (+3) (once per world per game)  
Defeat Black Phantom NPC (see above) and 1 Primeval Demon without  
returning to Nexus. (+6) (once per
game)
Defeat Black Phantom NPC (see above) and Primeval Demon without
returning to Nexus, and then defeat 1
Boss. (+7) (once per game)  
Kill an invading Black Phantom  
Ressurect a summoned Blue Phantom  

Note: To maintain White Tendency after defeating a boss (approx 45% shift to White), then go to the Nexus and commit suicide in the Nexus. Death in body form in a world equates to a (30%) shift back to black tendency, undoing all the effect of killing the boss. Towards Black

Die outside the Nexus while in Body form (-1)
Kill Old King Doran (-2) in 1-1
Kill the Body Form of one of the 5 special named NPCs that appear in Pure
White World Tendency
    Kill Body Form Executioner Miralda (-3) in 1-1
    Kill Body Form Scirvir, the Wanderer (-3) in 2-2
    Kill Blue Phantom Lord Rydell (-3) in 3-1
    Kill Body Form Satsuki (-3) in 4-1
    Kill Body Form Selen Vinland (-3) in 5-2

 Suicide in the Nexus in Body Form (+0) This affects World Tendency in
 the Nexus, but there are no World
 Tendency events there.
 Suicide in the Nexus in Soul Form (+0)
 Die in any world in Soul Form (+0)
 Kill the Vanguard (+0) in 4-1

Source: http://demonssouls.wikidot.com/world-tendency

Next, there are also the Mephistopheles Quests and Yurt, The Silent Chief. The Mephistopheles Quests appear if you kill Yurt, and have Black Character tendency. She will offer you assassination quests to kill many of the NPCs in the Nexus, and rewards you for doing so. Of them, the only unique item is the Foe's Ring. It should be noted that the NPCs will not respawn if you kill them. So doing so is not a good idea before the final boss.

Yurt is related to the above, but slightly differnt. You find him locked up in 3-2, and upon freeing him he will begin killing NPCs (the ones that Mephistopheles wanted you to kill, as well as a few more).To unlock him you need to take an alternate path through 3-2, so it is very possible to miss him. Killing him will grant you the Gloom Set.

There is also the Demonbrandt obtained by fighting Old King Doran. He is located in World 1-1, and you need the Demonbrandt to later obtain the Northen Regelia.

On a final note, the game doesn't force any items on you, and so it's possible to miss more then this on your way through, but for most items you can normally still get them if you just revisit the level.