When dedicated hosting was introduced, it was considered to be the best. Though at a high price, its benefits were unparalleled. It provided, and still provides, the benefit of security and safety of data, more space and bandwidth, freedom from unwanted ads, surety of site being live all the time. But today, with the entry of VPS hosting, it has lost its very much earned popularity. VPS hosting provides the same privileges as of dedicated server hosting, but not to the same extent. But, since the price is cheap, customers go for VPS hosting with the option of upgradation of the service if required. Still many big businesses are going for dedicated hosting, but that time is not far when it will be long gone.
Can agree that VPS is cheaper than dedicated server hosting solution, but I believe that you will have more advantages and privileges if you have Dedicated server package.
Actually, I would argue that dedicated servers aren't taking a hit, rather shared/reseller hosting. Somebody can get a VPS for the price of a reseller hosting account, with much more features and much more control. People who need dedicated servers are still buying dedicated servers, without a doubt.
The amount of shared clients that need more than a shared account can provide, but don't need a dedicated server have increased, so VPS accounts have certainly increased. The need for dedicated servers is still there though, because it takes a dedicated server to create the VPS containers, so it hasn't really "taken over".