At this point it is not clear how much of an impact on rankings the +1 button is having, but it appears to have more of an impact when someone within your social network +1's some content you search for, so at this point the affect appears to be more personalized.
I would expect as Google learns more about how people are using it, and is able to discern better real from spam +1 clicks then it will become a more important signal within the rankings.
How will it affect SEO and results? Google said:
Content recommended by friends and acquaintances is often more relevant than content from strangers. For example, a movie review from an expert is useful, but a movie review from a friend who shares your tastes can be even better. Because of this, +1's from friends and contacts can be a useful signal to Google when determining the relevance of your page to a user's query. This is just one of many signals Google may use to determine a page's relevance and ranking, and we're constantly tweaking and improving our algorithm to improve overall search quality. For +1's, as with any new ranking signal, we'll be starting carefully and learning how those signals affect search quality.
Google Plus One Publisher Button Launches