From the new game plus page on the demons souls wiki:
What will be carried over
The following items will carry over from one NG lifecycle to the subsequent NG lifecycle (e.g. from NG+ to NG++)
- All Consumables and Upgrade Stones. This includes Eye Stones, which enables you to summon phantoms in 1-1
- All Demon's Souls
- All Weapons, Armor and Shields
- All Miracles and Spells, your memorized ones will also remain the same
- World Tendency
- Character Tendency
- Soul Level and Stats
- Worlds 1-3, 1-4 and False King will be accessible without defeating any Archdemons (after completing 1-1 and 1-2, however)
The items mentioned above include those stored with Stockpile Thomas.
What will not be carried over
- All NPCs will reset to their default position, this includes all who have died for whatever reason.
- All Keys will reset to their default position.
- All doors and unlockable areas will reset.
Note: If you have the World Tendency requirement to open an area such as the execution grounds in 1-1 (Where Miralda is) when you complete the game, upon starting NG+ you will find that area open already. Although the door will have shut when you finished the game, the game will take into account your WT upon starting NG+ and will unlock/open any areas as normal.