This is a screenshot of the default cygwin bash prompt:

Copying and pasting is not intuitive, you can’t stretch the box horizontally, and most importantly, it breaks the illusion that I’m on a Unix box. But a better terminal option exists! When you install cygwin, you can also install the rxvt package. After installing the rxvt package, try this in a DOS window:

C:cygwinbinrxvt.exe -fg gray -bg MidnightBlue -fn "Lucida Console-14" -e bash --login -i

You should see a terminal like this:

As far as I can tell from my experience, this terminal acts exactly like a regular rxvt terminal on a linux box. I can highlight some text with my mouse, and then paste it by hitting either shift+insert or by hitting the middle mouse button. I can resize the terminal horizontally and vertically.

I set up a taskbar icon so that I can get that rxvt very quickly. The icon before the right-most icon will start an rxvt terminal for me.

Setting it up was really simple. I made a new shortcut by right-clicking on my desktop, then I copied this text:

C:cygwinbinrxvt.exe -fg gray -bg MidnightBlue -fn "Lucida Console-14" -e bash --login -i

into the target field:

Then I hit OK, and then dragged the new shortcut into the taskbar, and that’s it!