I've sold an affiliate site for $xxxk after being contacted directly and asked if I'd consider an offer. Previous to that I had no real desire to sell, hadn't crossed my mind. The buyer got a decent package and I got a decent price, this sale would never have occured using a site marketplace.
From a buying point of view (medium to high value):
Pick a niche you know and like, research the top keywords for said niche and start making a list of potential sites on pages 1 and 2 you think may sell. You need to be interested in the business, don't buy purely on $$$, it will dwindle away.
Sites with outdated designs are obvious targets.
Sites with good ranking subpages for decent keywords usually show the site is in a good standing and easily expandable.
Aged sites with a good solid search engine presence won't need much work to maintain the rankings, nothing urgent anyway.
Sites that you know you can instantly improve the income for. It's no good buying a site and having no idea how to improve it overnight.
Don't pay more than 3x annual profit unless the domain is gold or the historical branding is gold, I know some sites go for more but finding one that's actually worth it and for sale is nigh on impossible. Personally I'd want to get in the black as quick as possible instead of several years down the line. Buy for 3x, get your money back in 2x or less, decent.
Only pay 2-3x+ for sites with at least 3 years of consistent and/or growing revenue. Much of a site's value is created from its history. Check out the industry as a whole too, look for any pending regulations/laws that may harm you.
Once you have the owner's confidence (NDA etc) either request access to the affiliate/sales accounts where possible or request accounting records, screenshots and so on. Get access to traffic stats and make sure they're legit.
Research the link profiles, find out about any existing link sales, any agreements with other sites, any agreements the owner has on a personal level with anyone involved (special % deals, customers etc).
Always use Escrow.com as previously mentioned.
For bigger buys, speak to the owner on the phone or at least find out as much as you can about them - who, why sell, what else they do. Try and get a sense of their honesty/desperation, it goes a long way when deciding whether to deal with them.
For very big buys you will need legal support, a contract detailing every aspect of the business, get out clauses, cooling off periods and general stuff only a lawyer can advise on is a very good idea and the expense is nothing compared to the potential outlay.
A non-compete while nice in theory isn't such a big deal in most cases, if the site you're buying has solid history and a status only time and money can achieve then some new clone won't harm you. If they have a mailing list and customer connections then that's a different story, rules need to be in place there.
That's off the top of my head from my previous experiences, I'm a little tired but I believe it's all pretty accurate