Theoretically possible, but OUCH. If your new hardware is much newer than your old one, you might encounter BSODs, or worse, Windows might not load at all. Note that the dumbf*cks who built Windows 8 'fixed' it so that you can only get to safe mode AFTER Windows has loaded.
Note that if you follow Phuzzy's method you might not have access to the old system folders. Windows lets you gain permanent access to those folders, but if you do that, the old Windows version won't work properly any more.
My recommendation is to save all your stuff to a pen drive or another HDD partition (not your current C drive). Avoid copying system folders like My Documents, Downloads, etc. Instead, open that folder, select everything in there, cut and paste to a new folder in the place where you are backing stuff up. Take your time doing this. Run searches for various file types to dig out files you've squirreled away somewhere and forgotten. Don't forget the files stored in app data folders and folders created by applications in My Documents. Browser login and passwords and favourites can also be saved and restored. Most important is your wifi password and internet connectivity info - I found that one out the hard way many years ago; never again. LOL Software licenses for your applications need to be backed up as well.
Once you're done, install Windows from scratch, formatting your old C drive in the process (or use a different drive altogether). SSDs are expensive but the performance boost obtained by using that as your system drive is massive. Highly recommended; even a 128GB SSD is worth it. You can use conventional HDDs for your files.