I don't know of any specific studies but my main site is a case in point. Advertising (not just Adsense) and anything else that takes a visitor away from your site has the potential to cost you a member (because they may never come back).

There is a delicate balance to achieve if you're trying to get sign-ups to your site while advertising to your visitors. It's important to communicate your member features clearly and in plain view (above the fold whenever possible) and to ensure that things like login, register and faq links don't get lost on the page. This is a balancing act and it can be a tricky one (balancing advertising revenue optimization with member signups or sales of your own products). Also, too many ads will make your site look spammy which can be a general turn-off to people thinking about signing up.

I have watched the resulting see-saw effect related to pushing ads too hard or not enough and the relationship to member sign-ups. There's definitely a relationship.

Yes, there is some relationship. I wonder if sites with Adsense ads (I mention Adsense since they are the most popular among webmasters) have also negative effects on possible linking activities. I noticed Bing recommended WebmasterWorld in their official statement about discontinuing their own forums -- would they also link to WW if it had been plastered with ads? Probably(?) not..

From my personal experience I suspect AdSense has very little effect. From the feedback I've received it's expected that a site will have advertising.

Remember, a site stands or falls depending on what a site visitor receives or perceives they receive. People don't become members of anything unless they are getting something. Site visitors are selfish that way. That's the unspoken contract between a consumer and the provider. So as long as they're getting something they'll put up with advertising to the extent of the worth of what they're receiving.

As far as Bing recommending WebmasterWorld, I am confident that the recommendation came because WebmasterWorld might possibly be the best community for discussion of Bing related issues. I feel that the lack of advertising had little to anything to directly do with the decision.

From my personal experience I suspect AdSense has very little effect.

Again, this is all from personal experience but where advertising can have an effect on sign-ups is when it starts to push membership features off the page or create such a visual mess that it's not clear what the purpose of the site actually is. My point is that there's only so much space on a page and if you don't find a balance between content, advertising and the promotion of your own member services, then something is going to dominate the normal reaction of the visitor. Instead of drawing people with content and hoping they leave on an ad click, you're now also hoping a percentage will stick around for the member benefits. Camouflage the member services with too many distractions (ads are just one potential distraction) and signups will decline. Push all your ads below the fold so people always focus on your member stuff and ad revenue will normally go down as a result. There is definitely a point of diminishing returns when you are trying to balance multiple goals like this.

And, yes, I agree, people expect some advertising in general. Point is to not let it distract from the other things you're trying to accomplish.

Yep, it all depends on the goals and finding the right balance is not an easy job :).

Do consider sensitive categories too, these can be an issue on the type of sites you mention.

A forum that I visit has had problems with inappropriate ads which has lead to members actively recommending ad blockers.

Oh, and while we're considering distractions, you've got to watch out for ads from your competitors.