You are asking the right questions: seems like we've been here before.
The big deal comes in two flavors: 1) cloud data centers designed to be multi-tentant and handle wildly varying loads and 2) cloud services business models offer a way to get services on a pay-as-you-go basis and through a self-service portal. What I really like is that neither of these models are brand new, but like a lot of things in the cloud, we are taking proven solutions from many areas and combining them together in a new way. Note that most enterprise data centers are NOT run like Google/Yahoo/etc. and therefore can benefit from using cloud based architectures and business models.
Why shouldn't you just buy a server and virtualize? You certainly can use this approach and a LOT of businesses will do exactly that (and be very happy). The day that you need additional capacity (compute or storage) beyond what you purchased or the day that you need to recover from failed hardware, would be the day that operating in the cloud would show benefits. When you run out of capacity, cloud services can very quickly allocate additional capacity from the existing pool. When failures happen, you can simply restart your app (many cloud service providers do this automatically).
Is cloud for everyone? Well, yes and no. We will almost all use some cloud based services everyday. Things like a Bing search or Facebook are good examples here. A small business might be better off hosting its applications in a cloud but if their current solution is meeting their needs, then the urgency to change simply isn't there. Some applications requiring high levels of isolation (PCI-DSS, HIPAA, etc.) will require a specialized cloud and may not want to move to a cloud service immediately.
I heard a good analogy from a customer based in Australia: at some point, we used to put money in our mattress but eventually we learned to trust banks and started putting our money in the bank; today, we are careful about using cloud based services but the day will come when we understand that the trust levels are sufficiently high such that we will simply use them.
BTW: I also have the gray hair and the molding stacks of punch cards to know that we are 'borrowing' a lot from our history. A good thing IMHO.