Can I exchange links to other websites within my adsense website?
Answers: If your website is has some content that attract others, you will get some credit mention linking from others that is interested within the subject.
Observation from recent development in search engines, exchanging links does not seem to be to help getting sites up in search engine ranking, survey engines are smart enough to determine if it is artificial linking and the ranking algo does not seem to favor this type of ranking technique.
However, thinking from the website point of view, if the connection exchange do benefit your website visitors (i.e. a resource that your site visitor might be interested in, that compliments your current site content), it is still consider a nouns as it is value adding to your website visitors.
Hope that help.
Sure.