SSDs are more reliable - with three times greater MTBF than spinning media. They can withstand 20G vibration while operating, consume about one quarter the power of similar spinning drives and can read data about three times faster at a maximum of 64MB/s. Seek times are also dramatically faster.
While the big market growth is currently for ultra-mobiles and high end laptops, there's plenty of room in the server market too. NEBS compliant systems are already getting these drives and it won't be long before they're more common in blade systems and other servers.
So when will we stop storing data on rusty platters? Not for years seems the most likely answer, price / storage density curve will still favor spinning drives until sometime around 2011, after that, you may have to visit a museum to see a hard disk drive.