Yes, that's exactly what I want. I want WinAmp to always open in the upper left corner of the screen.
I don't know why this is not happening for you.
Assuming the program itself has been written to "remember" its size and location (wherever you dragged it to last, before you closed its program window) it should restore itself to that exact same desktop location the next time you open it up.
Winamp in particular absolutely does remember its location, but it has some "skins" and other further GUI characteristics which don't really allow re-sizing in the usual rectangular window fashion. Also, Winamp's GUI causes a "snap" to neighboring windows of itself (e.g. Playlist Editor, main Winamp window, Media Library, Album Art... these are all separate Winamp Windows but can "magnetically snap to each other" if you want) if you get them close to each other.
But if you simply move the main Winamp window (with the others closed for the moment) to where you want it to be, and then close the program, when you next open it you should see it exactly where it last was.
Other programs which have more conventional rectangular window GUI presentations than Winamp should absolutely remember both (a) where they are located on the desktop from wherever you dragged the window to, and (b) the SIZE of their outer main window, however you resized the window by dragging on edges or corners.
Of course, not every program has been written to "remember" its size and location. And unfortunately these do tend to open up by default in the center of the desktop, with a default size. This is not a Windows problem... it's an application/vendor program coding style problem. Take it up with the vendor.
But for Winamp... you can absolutely move it anywhere and it should remember where it is the next time you open the program. But again, Winamp has some GUI oddities because of its multi-window presentation, along with the "magnetic snap" behavior of its window, either to each other or to the edges of the desktop to the physical screen.