There are some people who will say that you don't need thermal paste etc. Case airflow also falls into this bracket since a heatsink will never dissipate heat effectively if the air around the heatsink is warm. In my opinion thermal paste is part of a whole range of procedures which together contribute to a cool-running system. However, the risk of this is miniscule if the thermal paste is properly applied which isn't difficult to do.

Obviously metals also conduct electricity and so can short out components on the motherboard if it does seep over. This mainly comes down to the fact that some makes of thermal paste use metal compounds in their paste since metal is a better thermal conductor. There is a risk of damage to the motherboard from excess use of thermal compound. The heatsink is obviously designed to dissipate heat from the CPU itself so the better the contact between the CPU and the heatsink the more heat will be dissipated and the cooler the CPU. It attempts to compensate for irregularities between the two surfaces - tiny microscopic bumps or ridges which may hinder proper thermal conductivity between the two surfaces. Thermal paste is intended to increase the thermal conductivity between the surfaces of both the CPU heatspreader and the heatsink itself.

Cpu thermal paste