Sponsored links are any links where the sponsor pays for placement. These advertisements are typically displayed above, and to the right of, search engine results or content. But they sometimes also appear below search results.
Google AdWords ads are labeled as "Sponsored Links", as shown here:
Yahoo Search Marketing ads use the "Sponsor Results" label:
While MSN Live Search ads use the "Sponsored Sites" heading:
Do Sponsored Links increase PageRank?
Sponsored Links such as Google AdWords, Yahoo Search Marketing and MSN ads use long and sophisticated tracking links which don't get crawled by Google. As such no PageRank is passed along the link.
However, many websites sell sponsored text links which use short links that link directly to the sponsor's website. These types of links are usually crawled by Google and therefore do attract PageRank.
Which websites offer Sponsored Links?
Google AdWords, Yahoo Search Marketing (add CJ link), and MSN AdCenter all offer Sponsored Links. Link brokers, such as Text Link Ads, also offer Sponsored Links, but of a different sort. Link brokers sell simple text links that link directly to your site, and therefore attracts PageRank. The linked anchor text is usually the keyword phrase you're trying to get top rankings for. However there is no accompanying description next to the link so they don't do as good a job of persuading people to click on your link.