Dofollow is the best type of backlink because it passes link juice from one site to another and counts the anchor text for keyword relevance. How SE treat nofollow:
DoFollow links tell the search engines to follow that link, that is, they tell the search engine that this link should be counted as a proper backlink. So this is good for SEO. NoFollow links are just good for real visitors as the search engines do not follow these links. Thus, you will not get any link juice for these links.
As the names show. DoFollow will deliver you the LINK LOVE and JUICE to give you good Google SERPS. NoFollow is useless for Google, but Yahoo might give you some credit. My advice: Concentrate on DoFollow, and forget about NoFollow
Dofollow is always good but i don't forget to go on Nofollow because you have to get some ratio of Dofollow & Nofollow links which makes your web seo afforts on the next good level.