First, don't try to use regex for this. The odds are really good you'll come up with a fragile/brittle solution that will break with changes in the HTML or will be very hard to manage and maintain.
You can get part of the way there very quickly using Nokogiri to parse the HTML and extract the text:
require 'nokogiri'
html = '
<html>
<body>
<p>This is
some text.</p>
<p>This is some more text.</p>
<pre>
This is
preformatted
text.
</pre>
</body>
</html>
'
doc = Nokogiri::HTML(html)
puts doc.text
>> This is
>> some text.
>> This is some more text.
>>
>> This is
>> preformatted
>> text.
The reason this works is Nokogiri is returning the text nodes, which are basically the whitespace surrounding the tags, along with the text contained in the tags. If you do a pre-flight cleanup of the HTML using tidy you can sometimes get a lot nicer output.
The problem is when you compare the output of a parser, or any means of looking at the HTML, with what a browser displays. The browser is concerned with presenting the HTML in as pleasing way as possible, ignoring the fact that the HTML can be horribly malformed and broken. The parser is not designed to do that.
You can massage the HTML before extracting the content to remove extraneous line-breaks, like "\n", and "\r" followed by replacing <br> tags with line-breaks. There are many questions here on SO explaining how to replace tags with something else. I think the Nokogiri site also has that as one of the tutorials.
If you really want to do it right, you'll need to figure out what you want to do for <li> tags inside <ul> and <ol> tags, along with tables.
An alternate attack method would be to capture the output of one of the text browsers like lynx. Several years ago I needed to do text processing for keywords on websites that didn't use Meta-Keyword tags, and found one of the text-browsers that let me grab the rendered output that way. I don't have the source available so I can't check to see which one it was.
