Info site. Many search results lead to detailed multiple-pages. I no-indexed the pages beyond page 1, (btwn 2-10 more) and improvement in SERPs was of the order of position 5 to 4. As Tedster said, gives a marginal kind of improvement; not as I expected.
But the gripe here, real, is that single page 'thin content' can serp better than multi-page detailed and higher quality multi-page results (the extra pages (generally a marker of more in-depth, quality) can count against you.
Where multi-page sections can be usefully divided by text / subheadings i do that. But in some cases the following pages are just images, and large ones. That's a big attraction and uniqueness to my site, so I don't plan to change this just for Google.
Yet in both cases, including long text over multiple pages, with correct headings etc, can be beaten by single-page thinner sites.
There is an upside, however, in the case of text on multiple pages when it comes to long-tail searches.
IF the comments by John Mueller do mean what we think, then this a bit 'shallow'; I see the point, but life is a bit more complex than that - the algo should be more nuanced (noindex is not necessarily hiding anything, just keeping the index to chapter headings, not listing every page, so to speak - it can be good sense / legitemate).
The instruction no-index does not imply no-read. If G is wise, they will not simply tally no-indexed page count but tally which are actually thin, or not - and I hope take into account non-text content (which I believe they can do).
So, if you noindex 80% of your site (I did so only because surprised it WAS indexed), one can expect a circa 20% improvemnt in serps (Actaul scoring might be more dramatic of course but a serp increase is no mean feat, and even a small increase welcome).
[edited by: bramley at 6:47 am (utc) on Apr 2, 2011]