I tried the suggestions above and none of them worked in my environment. (Windows PuTTY clone over ssh)
Some additional googling turned up:https://unix.stackexchange.com/questions/110684/copy-paste-into-sshd-vim-from-local-windows-clipboard
One of the comments suggested using SHIFT+INSERT which did the trick for pasting from my desktop's clipboard into Vim's buffer. Ctrl-C was already working to copy to the desktop's clipboard from Vim.
