At least for me, I find that the majority of my copying/pasting and other kinds of text editing is done while using the keyboard to compose something (an email, for example). In those situations, the answer is simply to use a keyboard with a text-editing mode. Swype (my keyboard of choice these days) has a very nice separate panel for editing, including not only copy/paste but cursor buttons for up/down/left/right, end, home, jump, etc. Works very well.
Another very good keyboard that includes editing features is Cootek's TouchPal, which I absolutely loved from back in my Windows Mobile days. Cootek just put a new version into the Android Market (it's free) that works perfectly on my Droid, and finally includes all the features of the WM version such as an editing panel, an emoticons panel, and something even Swype doesn't have: the ability to predefine frequently-used strings like Web URLs or email addresses for entry with a single key. TouchPal also lets you swipe between a conventional QWERTY, a phone keyboard with 3 letters/key, or my favorite which is a QWERTY layout but with two letters/key - TouchPal figures out the desired word quite well, and it's easy to type fast with the much larger keys. (The Market entry for TouchPal says something like "TouchPal for Chinese language", but the default is English.)
I sympathize with the OP - I remember how utterly frustrated I was when I first came to Android after many years with WM, which had far better copy/cut/paste features.
I'm also going to check out the "Copy Paste It" app for the occasional times when I do need to copy from outside of an editing window (from a web page, for example).