I think Titanium Tetrachloride would be a good option for white smoke (I've heard it's used quite often in smoke bombs). But it releases quite a lot of $HCl$ gas and so it might not be very safe.
A quick Google search comes up with a lot of answers to your question though. This site even answers your question in the same context (The elections going on at the Vatican):
Apparently you can make white smoke using Magnesium powder as well. (The white colour is due to fine particles of Magnesium Oxide $MgO$ )
It seems the Vatican has experimented using many sources before (Military flares, Smoke bombs and so on) though apparently they didn't turn out too well...
The Wikipedia article on Coloured smoke gives another possibility. You can add Titanium Dioxide ($TiO_2$) to a mixture of Potassium Chlorate ($KClO_3$) and Lactose for white smoke. $KClO_3$ is a powerful oxidizing agent which reacts with Lactose (which is a reducing sugar) to create an explosion. $TiO_2$ is safe and is used as a pigment in most white paints and as a food colouring as well.
The official recipes have been revealed by the Vatican press office. See this story on the New York Times website.
The previous edit was partially correct. They use a mixture of $KClO_3$, lactose and pine rosin for white smoke. For black smoke, they use Potassium perchlorate ($KClO_4$), anthracene (an aromatic compound made of three fused benzene rings) and sulfur.
The process (quoted from the site):
"The chemicals are electrically ignited in a special stove first used for the conclave of 2005, the statement said. The stove sits in the Sistine Chapel next to an older stove in which the ballots are burned; the colored smoke and the smoke from the ballots mix and travel up a long copper flue to the chapel roof, where the smoke is visible from St. Peter’s Square. A resistance wire is used to preheat the flue so it draws properly, and the flue has a fan as a backup to ensure that no smoke enters the chapel."