Hi John,
Sharepoint WebParts are similar in concept to ASP.NET WebParts but they are not compatible. Sharepoint WebParts caught on but ASP.NET WebParts did not. There is a market for 3rd party Sharepoint WebParts but not for ASP.NET WebParts.
The My Page feature is still there if you want to use it, once I split it off from the core, then you could actually fork it and modify it as you see fit.
There are things out there that are similar such as the DropThings project, but I'm not sure about how easy it would be to integrate, it isn't something that interests me at the moment. It isn't using WebParts but it has similar drag and drop kind of thing similar to netvibes or MyYahoo or iGoogle.
Best,
Joe