Gravestone

An urn or gravestone appears on the lot when a Sim dies. An urn can be placed on the floor or on tables and counters. A gravestone can be placed on the ground outside. In The Sims, The Sims 2, and The Sims 3, whether a grave appears as an urn or a gravestone will depend on whether it is inside or outside; an urn will become a gravestone if it is moved outside, and a gravestone will become an urn if it is moved inside. Sims can "Mourn" over graves or urns. Beginning with The Sims 2: Nightlife, they can be moved to a community lot.

The Sims
In The Sims, different gravestones are available, but players have no control over which one appears after a Sim dies. Pets and famous Sims have their own urns and gravestones.

Graves cannot be placed on community lots. "The Gothic Quarter" in Old Town, and "Vernon's Vault" and "A Spooktacular Spot" in Magic Town all contain gravestones, but they are simply decorative and are not linked to any Sim's ghost.

The Sims 2
If a Sim had platinum aspiration when he/she died of old age, a gold gravestone/urn will appear with the dead Sim's aspiration symbol on it. Otherwise, the Sim will get the average, gray gravestone/urn.

If Nightlife or later is installed, players have the options to click on an urn or gravestone and select "Move grave(s)". This moves the grave to a community lot of the player's choice, where it will appear near the telephone. When this is done, the shade of the Sim will appear and wave goodbye, then the grave will disappear, and the player will be notified that the Sim has died on another lot and will return in spirit to the place of their death. It appears that this may refresh the tendency of family members to cry over the death, even if that had largely passed. Another way to move a grave is to place the urn or gravestone in a Sim's inventory, and send that Sim to a community lot. If player clicks on the ground and selects "Place NAME's Grave Here", the Sim will go to that spot, and the grave will appear there. Regardless of which method is used, the player will be able to select that lot from the neighborhood view, and use the hand tool in Buy or Build mode to place the graves where they wish.

It is a good idea for players who plan to move graves to make a cemetery, but there is a pre-made cemetery, "Gothier Green Lawns", found Downtown next to the House of Fallen Trees.

In The Sims 2: Pets, pets get gravestones/urns that are marked with a pawprint, and the owner(s) of the pet will get a special memory. A pet's urn is gray, and a pet's gravestone is brownish.

The Sims 3
In The Sims 3, there are at least 3 different types of gravestones; a flat plaque-like one, a gray one that's similar to the ones in The Sims 2, and a tall obelisk-type one. A Sim can obtain these different gravestones by:

Small Plaque
 * Dying before earning 75,000 lifetime happiness points.

Medium Tombstone w/ Plaque
 * Dying after earning 75,000 - 149,999 lifetime happiness points.

Large Tombstone w/ Plaque engraved
 * Dying and earning +150,000 lifetime happiness points.

Also Shift ctrl clicking will give the option to change the cause of death A gravestone will have a plaque which shows the cause of the Sim's death:

When a Sim dies, the player has the option of whether to keep the grave on the Sim's home lot or to put it into a Cemetery. Also you can get Tombstones and Urns with buydebug on known as "Remains", however, they will not contain ghosts.