How can I get a block cursor in Vim in the Cygwin terminal?

This question on the Cygwin mailing list answers the question by setting some arcane variables to the appropriate escape sequences. Add this to your .vimrc:

let &t_ti.="\e[1 q"
let &t_SI.="\e[5 q"
let &t_EI.="\e[1 q"
let &t_te.="\e[0 q"

There's a setting for that, in the cygwin terminal emulator:

Right-click on the window title bar > Options > Looks > Cursor > Cursor radio button

Create a file ~/.minttyrc, add below line to it

CursorType=block

Then re-launch mintty, which is Cygwin's default terminal.