Helping people with computers... one answer at a time.
Pasting web page content into Word certainly isn't guaranteed to maintain the same formatting, but adding underlines to everything is probably a bug.
Quite often, I find a piece of information via a newsletter or on the Internet that I want to keep. My normal routine is to select the text/graphic that I want, press Control>C, open a new Document, and press Control>V. Depending on the source of the text/graphic, I will get exactly what I want -- a nice clean paste of ONLY text and/or graphic. However, when copying and pasting from some websites and/or newsletters (yours included), I get the text and graphics, but all of the text is 'underscored' and I can't get rid of the underscores. If I select 'Paste Special' and save as .rtf, I will get text without underscore but no graphic. What's with this and how can I avoid the underscores?
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I was able to reproduce something that sounds like what you're seeing. I'm not sure that it's exactly the same, but I'll describe what I think is happening (hint #1: it shouldn't) and what you can do.
And Hint #2? They might look like underlines, but they're not.
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Let's start with an article on my web site and select a portion of it to copy:

Here, I've selected the summary line through the text at the bottom of this screen capture.
Ctrl+C copies that to the clipboard.
In Microsoft Word, I type Ctrl+V to paste what I just copied into a new empty document.

And sure enough, some of the text appears underlined.
Except ... those aren't underlines.
Those are revision marks.
The clue that makes me think that revision marks are the problem is that the underlining is continuous and there's a revision mark bar down the left-hand side.
Now, here's the problem that I see:
I didn't have revision marks enabled.
Even if I had, I'd expect that all of the text would be treated the same way.
Revision marks, when enabled, are intended to indicate what text has changed in an existing document. Changed words are typically colored differently and underlined and the revision mark bar is placed along the outer edge of the page at the position which the changes occurred.
As I said, when enabled - which they are not.
The best way to remove revisions is to tell Word to "accept" all of the revisions.

Click the Review tab in the Word ribbon, then click the Accept button, and finally choose Accept all Changes in Document.

The unexpected underlining is gone.
To be honest, I believe that there's a bug in here somewhere.
One clue is exactly where the underlining started.
When I look at the page from which I originally copied the code, an advertisement sits in between the text that is not underlined and the text that follows, which is underlined. Even though it was not highlighted in the copy operation that I started with, it was included.
I believe something in the material copied erroneously caused Word to turn on revision marks when it was pasted in due to that advertisement, even though the revision mark indicator still showed that they were off.
Even though accepting all changes is a pretty simple solution, my theory is that when you select part of a web page to be copied, avoid advertising blocks.
A couple of tests here seem to bear that theory out.
Article C4849 - June 17, 2011
Paste special/unformatted is very useful, but sometimes too drastic. One of the types of formatting which I find bothersome is the way in which copied web-pages often show up as big tables in Word. I recently discovered that these can be easily be turned into text with the "Convert table to text" command, shown in the Table menu in Word 2003.
Posted by: Bernard Winchester at June 21, 2011 3:57 PMI use ClipMate from Thornsoft as my clipboard. It has a function that will strip out everything but text.
Posted by: Will Thomas at June 22, 2011 8:15 AMThanks Leo. I had the same problem but wrongly assumed the underlines were the result of copyright protection.
Posted by: Bob Grot at June 23, 2011 12:20 PMThanks Leo. I also experienced this but didn'nt have the foggiest notion of what was happening.
Posted by: Anwar Kabir at June 24, 2011 7:02 PMOne of the commenters mentioned that copying "bottoms up" works better -- I second that! For some unknown reason I almost always get cleaner results doing it bottoms up than top down.
Posted by: Geoff Walker at June 25, 2011 2:50 AM