Ghost baby

In The Sims 3, it is possible to "Try for Baby" with a ghost and spawn a ghost baby.

Making it Happen
There are several ways to achieve a ghost baby. One way is to talk to a non-playable ghost every night when it appears at the graveyard or your house (if you have an urn or tombstone on the lot) and build a relationship to atleast "romantic interest", then if the ghost is in your house, you can try for baby there. However, if the ghost is at the graveyard or other public lot, you will have to either steal their grave (must have a sim with the Kleptomaniac trait) and put it on your current home lot, or marry the ghost to add it to your household. Having the ghost in your household makes this process much easier because you can interact with them at all times of the day.

Another way to generate a ghost baby is to kill off one of your sims and get their ghosts to be playable. To do this you must wait until after the sim has died, then wait for an opportunity called "Oh My Ghost!" this will allow you to take the remains of the dead sim and create a playable ghost of them. However, you can make a ghost playable with one click or even instantly make a regular sim into a ghost with the use of mods, like this one:

If you need help on quick and easy ways to kill your sims and make them ghosts without mods here is a good tutorial:

What They Are
Ghost babies conceived either from a ghost female or by a ghost male are NOT immortal. They will age just like every other sim, and even "die" of old age. It will actually say that the sim has moved on to the Netherworld and you no longer have control of the ghost. Ghost children even have their own tombstone, so if they want to to they can click on it at anytime and select "Return to the Netherworld" if you want them to no longer be a playable sim. Non-playable ghost do not age, however, but as long as the ghost is listed in your household they will age up like every other sim. Some special things about ghost sims is that you will hear odd whispering noises when they are around and they will randomly scare others at times.

What They Look Like
There is a 50% chance that your sim will conceive a ghost baby (that is, unless, both parents are ghosts, then it will always be a ghost baby). Currently there is no known way of increasing the chances of having a ghost baby instead of a regular sim baby. If the baby looks like a normal sim, it will be completely normal in every way, the only strange thing you might notice is (as with all ghost offspring) their ghostly parent will appear as dead on the family tree. The baby can, however, inherit the skin, hair, eye color, and other traits from the ghost parent. For example my African American sim had a child with a ghost male, and the baby came out as a lighter skined African American child. This is because the ghost male had light skin. If you do conceive a ghost baby, it will be the color/type of ghost that the ghost parent was and will look exactly like a normal ghost, only it can age like regular sims. It will also appear as dead on the family tree. If you have two ghost parents, the baby will be the ghost type of one of the parents. There is no way to mix colors of two ghosts.