Try searching on google or forum first before you post such questions. Dofollow links pass PR and are counted as a vote for the website. Nofollow will not pass PR.
Have you ever tried to search DP for an answer to a question? Next to impossible to find what you need. Google may work but that is what a webmaster forum is for to ask questions and learn. @ the OP Here is a great article to help you undersatnd Back Links . As the name applies, Google follow do follow links and they do not follow no follow links.
You can see which links are do follow and no follow at a glance without having to check the page coding by using firefox SEO tool too. Check it out.
I frequently use DP search (only forum search works, overall search almost always times out) to locate a thread that I had found interesting but forgot to bookmark. In OPs case a simple search for dofollow or nofollow will give the desired results. I understand that most webmaster forums (and others too) thrive on same question being asked again and again and I don't mind that but at the same time we should put an effort that only ignorant people ask such questions and once they do they can be told to use search as well @OP: sorry for hijacking your thread. Google will index a page that only has nofollow links but they won't give weight for the links to this page.
NoFollow was invented to prevent spammers from randomly commenting on blogs for more backlinks. Basically NoFollow backlinks don't improve your site's PR at all. DoFollow just means that the rel="nofollow" tag is not there.
Having said this, although you don't recieve PR you can still recive "trust" credit for getting no follow links from established sites such as Wiki - you may also get a little bit of traffic through these links and every little helps
No-follow are not beneficial as Do-follow. The links to your site form the dofollow links is counted into backlink whereas nofollows links are counted as visitors or traffic source.