What's the likelihood of the existence of unknown elements in the Solar System? What's the chance that there might be undiscovered chemical elements in the Solar System - either on planets or around the Sun or on asteroids of the Oort-cloud?
As far as elements (e.g. on the periodic table) go, I would say the odds are very slim.  We already discovered or produced all the elements of the Periodic Table up to atomic number 112 at least.  As the number increases, the half lives of the elements generally decreases, and is very short for elements above 102. If this trend holds true as the number increases, practically all the "undiscovered" elements should have turned into the lower known atomic number elements.

However, there is hope.  There is a theorized "island of stability" where a narrow range of yet to be discovered high atomic number elements may be stable: http://en.wikipedia.org/wiki/Island_of_stability
I would say there is a slight chance this element could be discovered in the solar system.