Disclaimer: [hand on heart] I do not encourage the practice of buying links in order to inflate Google PageRank. Links should only be purchased for advertising purposes and should always be identified as such via the nofollow link attribute.
That said, being a pro link builder, its in my clients best interest if Im experienced in ALL forms of link building. Plus, being in the trenches, I see hundreds of (what I suspect to be) paid links on a daily basis and Im often up against competitors who have huge link buying budgets.
For these reason, Ive been getting acquainted with the world of paid links and the certain factors they can influence, through experimentation on some of my personal sites.
Without giving away too much, here are some of the things I've learned during my foray into the world of link buying:
1. When it comes to ranking, most paid links DO work. 
Yes, even blogroll links btw. Sorry Google, I know youre really trying, and in a lot of cases winning, but I continually witness way too many instances of sites buying hundreds of craptastic links and then ranking for their term(s). Even in competitive niches and, in some cases, for the long-term. The problem being that its still too easy to fly under Google's radar, probably due to the fact that they have BILLIONS of webpages to police (thats their doing though, not ours).
For just one example, there is huge business in people buying links from high PR dropped domains - whose new owners have thrown up some horrible, nonsense automated content and started cashing in.
Granted, these types of dropped domains do appear to get caught some of the time (as noted by their sudden and complete loss of PR), but perhaps by coordinating directly with domain registrars the success rate could be greater. Like I said, at least Google is trying though, which brings me to my next point
2. Dont buy links that look obviously paid.
Seems like a no-brainer but I've seen evidence of sites being penalized for selling links and theyre usually the ones that dont try to hide it. This means, stay away from sites that have even a few spammy type paid links (casino, pharmaceutical etc) or links that arent on topic, even if youre tempted by the sites deliciously high PR. This is especially important if you don't want to be throwing away your money.
Also avoid being listed under headings marked advertisers or sponsors or on a blog that openly proclaims that they publish sponsored posts or paid reviews. It stands to reason that examining surrounding text is the most basic method that Google uses in an attempt to flag paid text links.
Instead of just buying where your competitors are buying (likely from paid link networks, which are cheap and readily available), try to hand-pick sites based on your own set of quality guidelines and then approach each of them about the possibility of acquiring a link. This way, if Google happens to catch the paid link network, your competitors links will be devalued but not yours.
Note: Most sites have never even thought about selling a link but theyre usually pretty willing if approached the right way 😉
3. Stay relevant. Avoid temptation.
If you plan to purchase backlinks for PR or ranking purposes, then further bypass any red-flags and distance yourself from the craptastic link buyers, by staying relevant to your niche.
Dont be tempted to purchase links from sites that arent related or logical to your products or services. For example, World of Warcraft links dont belong on a health blog, Weight Loss links shouldnt be geared towards Anorexic's, and since when is Lasik Surgery for babies?
Remember, if it doesnt make sense to real people, chances are it wont make sense to Google either.
4. Mix things up.
I mentioned that paid blogroll links still have their use but so do links from resource pages, friend listings, partner pages, 'donor' listings, within blog posts, articles, glossary's, research credits, etc, etc.
In a natural link setting, your links wouldnt all come from the same type of sites therefore, when paying for links, try to keep things looking as natural as possible by mixing up your link sources. Even pay for a few nofollow links here and there.
5. Instead of offering to buy a link, offer to donate for or sponsor.
I found this particularly useful for high-quality prospects (.edus, .govs etc) that would most likely be offended at the offer of money in exchange for a link. When your communication is worded properly, sites such as these are generally open to listing a good resource such as your site, especially because you were so generous in donating to their department or sponsoring their team for example.
In the end though, as the link buyer, I believe you have less of a chance of being caught and spanked by Google than the link seller does. This is because; as much as Google may be able to tell that a site is SELLING links, it cant definitively prove that a site owner is in fact BUYING links. After all, it could be a competitor out to ruin you and besides that, we simply cant control who links to us much.
Now that Ive seen evidence that paid links can get me the long-term rankings I need (as long as I keep buying), will I be completely abandoning my trusty manual link building techniques? Not a chance, as the world of paid links is still too dodgy for me. It doesnt mean that I wont be creating my own paid link opportunities where ever possible though.