I use link exchanges occasionally and the sites that I've used it on are still ranking fine.
I've always been VERY picky, even if the prospective link partner is ranking. Even if the site looks a perfect fit, if they have one dodgy or irrelevant looking link partner (SEO company, overseas business, low quality directory) I pass. If they're a member of a link trading network I pass. If they're doing anything 'aggressive' or poor quality on their site (over-optimised perhaps, or too many pages or too thin content) I pass.
And I'm and very careful to mainly use the brand or website name for the link, with the odd keyword as part of the anchors.
Are you doing a link exchange to boost Pagerank? - Bad idea
Are you doing a link exchange because the traffic is likely to convert - Good idea
Are you doing a link exchange to boost your rankings - Bad idea
Are you doing a link exchange because it provides a relevant resource useful to your audience - Good idea
Most people that do link exchanges are using an outdated seo mentality from 10 years ago. They can't accept that things have changed and will continue to change. Links are still valuable (just look at how much referral traffic comes through relevant links) but Google is no longer a simple formula that is easy to trick. You need to be careful and make smarter business decisions. Not every link is a smart link but there still are many good opportunities.
I haven't engaged in link exchanges for myself or clients for at least eight or nine years. My only linking that may appear unnatural to Google is reciprocal linking between my site and a client's site (site credit link on theirs, link from a portfolio page on mine). And even then, I've been cutting back on doing that, because it won't appear "natural" to Google.