Silver is a better conductor of heat than copper, but not by much (only about 10%) - this works out at about a 1-2 C change in temperature by converting a copper heatsink to silver.
Silver also comes with a huge cost penalty, weight penalty and has problems with corrosion. In general, it's too much cost and trouble for too little benefit.
(Everytime we discuss this issue of heatsink material, someone always comes up with comments about how well metals 'give up heat' or 'hold onto heat'. The thermal capacity is irrelevant in heatsink design - all it determines is how quickly the HS warms up when the CPU switches on, and how quickly it cools after shutdown.)
Modern heatsinks make increasing use of heat pipes. The big advantage of heat pipes is their incredible thermal conductivity - this allows heat to be moved relatively long distances, permitting the use of heatsink designs that don't depend on connecting fins directly to a heat spreading slug. (While silver is about 10% better than copper, diamond is about 200% better, heat pipes are about 10,000% better). The use of heat pipes allows much more flexibility in design, by essentially avoiding the limits of thermal conductivity - the problem then becomes one of how many fins you can cram into the available space and airflow.
There is still the issue of the heatsink base - there may be some benefit in replacing a copper base with silver - but as the limiting factor is likely to be the fins, this is unlikely to be worthwhile.