Do not copy (Ctrl + C) and paste (Ctrl + V) text directly from a web site unless you want the exact formatting of that text in your document.  Web text includes HTML formatting that will not match your document.

Under the Edit menu you will find Paste Special, which has various options for pasting selections you have made from Web sites (or HTML email programs).  The Unformatted Text option will insert only the text without any formatting into your document using your default paragraph style.  Create a macro to make this task much faster.  You can find various copy/paste macros in the MS Word macros forum on Productivity Talk. 

A quick way to remove leading spaces at the beginning of each line is to select the text, center justify (CTRL + E) the selection, then left justify (CTRL + L) the selection.  All the extra spaces disappear.

Another way to remove HTML formatting is to paste text into a program like Notepad, then copy/cut and paste into your Word document.