(1) They are very, very, very rare as compared to other metals found on this planet.
Imagine this : You have to remove 9.39 tonnes of earth to get one golf ball weight of gold.
(2) The most important reason is that these metals are called noble metals. This is because these metals do not react (or react very slowly) with oxygen in air to form oxides.
You may have seen the rusting of iron, or a green layer on copper (due to oxidation). The noble metals are inert to this reaction and thus remain all shiny and new for years.
(3) These metals are resistant to corrosion by the action of acids or alkalies on them.
(4) They are ductile and have high lustre (which adds to their value).