On composing a new email while in Exchange ActiveSync, GMail or Hotmail (setup as an email account) I can do this while typing.I think that trick only works from a text box. Long pressing on text in an email does not work. The only way I have found to copy text from gmail is to hold down shift while I drag my finger over text.
I can also do this in the built-in Facebook App while entering text into fields. Everything else in FB is a link and not plain text.
As for highlighting text you're reading while in the browser, you have to hit the Menu button followed by Select Text followed of course by Menu and Paste into a text field someplace.
Texting doesn't have C/P ability on the Droid but emails most certainly do.