Should not be any correlation at all. If there was, not only would there be an ethical argument, there may be legal repercussions as well.

A few things:
First: "Correlation does not equal Causation"

It is possible that buying Adwords ads can negatively impact your ranking for the specific keywords. There have been reports here in the past of people experiencing a drop in organic traffic after beginning to advertise. This is due to cannibalization. As the ads appear above the organic results users find your content with the ad first and thus click on it and not the organic result. So fewer clicks on the organic links versus the competitor's. The competitor may then gain in ranking. Net traffic to the site should be up, but organic traffic will be down. This is of course pure speculation based on anecdotal evidence.

An inverse argument can be made as well. Since users are seeing more of the advertised brand, they may learn to trust and then link more the site. So by this logic Adwords should help rankings.

In both cases any influence Adwords has on ranking will be indirect at best and likely not measurable in any meaningful way.

Correlation does not equal Causation

Good point NickMNS

Is there any correlation between .. spending on adwords and getting & maintaining reasonable organic listings?

They are different worlds whose orbits do not cross.

Any relationship between organic ranking and AdWords spend would be indirect. If ads bring visitors to your website, and some of them talk about it, over time you'd gain links and other signals that (probably) strengthen your organic performance.

That could be said about ANY promotion, of course, and it's why savvy promotion is part of SEO these days. If AdWords brings any magic to the mix it's the quality of targeting that can be achieved.

Keep in mind that organic performance often depends as much on what your competition is doing as on what you do. You could be doing 100 things right but still fall behind if a competitor is doing 101.

But do people who are spending on adwords get nasty organic penalties?
Or does google say to itself, these are my customers so I won't penalise their site in the SERPS?

Your question really asks whether Adwords spending records are accessed by and used in an algorithm component. That seems unlikely to me. Keyplyr's point about ethical and legal implications is not trivial. It means

1. Google is in a difficult and potentially very costly position if caught using Adwords spending data in this way and
2. They cannot advertise that they are doing it, so can derive no benefit from it.

Indirect effects, however, as buckworks points out, are not only possible but likely.

Hi keyplyr "Should not be any correlation at all. If there was, not only would there be an ethical argument, there may be legal repercussions as well."

I am pretty sure companies respond to fluctuating SERPS listings with Adwords spending. They need to be up there in the SERPs page and I bet each time there is an algo change that penalises bricks and mortar businesses, many of them will simply respond with increased Adwords campaign spending.

And why not? nothing is free, those B&M businesses will be paying someone for SEO, and or they will be paying Google for Adwords. It is in Google's interests to persuade the B&M company to pay G for adwords, rather than have them paying some independent SEO somewhere for seo.

Well now you've changed your perspective. My reply was specific to the premise of Google controlling SERP according to Adword spending, where you said...

google changes the organic listings in part to stimulate adwords spending

Oh, I don't mean to change my reasoning, sorry about that.

Originally I wondered, 1) do people who spend on adwords get some level of protection against organic penalties because they are "paying customers" of google?

However I also wonder, 2) do changes in the SERPS motivate businesses to spend more on adwords? and can this be a motivation for G to mix things up when they do algo changes?

To nickMNS, yes, you make a good point, re canibilisation, I had not considered that.

to buckworks, also good points, thank you. And even within adwords competitor activity affects adwords rank via CPC. As to whether these two worlds are separate, G knows all I am sure, but whether G relates adwords activity to organic results is what I am wondering.

Hi Wilburforce, yes it would not do for such a relationship to be public, and I am I suppose assuming that it does not exist,

But in other worlds there are relations between advertising and free listings. For example if you are trying to get some free editorial in a journal, their advertising people will normally start talking to you and it is implied that if you take out a small advert their editorial people are likely to look more kindly to including your editorial content in the publication. Of course they will all state that this isn't the case, but the strong feeling is there.

So translated to the G situation, it might be that if you spend on adwords, your organic rankings would not suffer. No more than that.

No one has come on yet to say that they spend on adwords AND had a massive penalty in the SERPS while they were doing that?

do people who spend on adwords get some level of protection against organic penalties because they are "paying customers" of google?

Not in my experience.

No one has come on yet to say that they spend on adwords AND had a massive penalty in the SERPS while they were doing that?

Alas, that IS in my experience ... spending 100K / month on AdWords in the same season as a drastic decline in organic traffic after a site revamp.

AdWords and organics really are separate worlds.

Fair enough buckworks, that is good feedback. Thank you.

No one has come on yet to say that they spend on adwords AND had a massive penalty in the SERPS while they were doing that

Not quite true. It goes with the seasons.

Sometimes the prevailing "wisdom" is that Adword customers are immune to penalties, and get great listings. I cannot see the logic myself, unless they could advertise the relationship, but anyway...

Sometimes the prevailing "wisdom" is that Adword customers are frequently stomped on, to get them to increase their adwords spend. This is makes more sense as a logical proposition, but I see little evidence.

... massive penalty...

spending 100K / month on AdWords in the same season as a drastic decline in organic traffic after a site revamp.

Arggghh, to see a mod spreading the "traffic decline == penalty" fallacy is... disheartening.

Edit for clarity / civility

Shadows, I missed a nuance and I stand corrected.

My point was that a $100K / month AdWords spend provided no protection against ups and downs in the organic rankings.

frequently stomped on, to get them to increase their adwords spend.

At the time our organic traffic dropped, we were already spending the most we could on AdWords while keeping a positive ROI. If we had pulled more traffic from AdWords by raising bids or reaching into less targeted places, it wouldn't have been cost-effective.

The organic traffic drop didn't motivate us to spend more on AdWords, it motivated us to test ads in new and different places.

Google doesn't win by stomping on potential advertisers, it wins when ordinary businesses find it profitable to advertise on AdWords. Those are the folks who will spend money month after month, year after year.

That's where the gold is! No conspiracies necessary.

If you do spend a lot on AdWords though, there will be an indirect benefit.

Your product/website could be spoken about in forums, word of mouth, linked to, all sorts. I've seen it a fair bit.