It will increase your rankings in searches for their backlinks. It will increase your rankings for terms they might include in their posts that you'd otherwise not mentioned in your site.
It will lower your PageRank score in Google.
It will lower your ranking for all of your own keywords in Google a little because it lowered your PageRank.
It could be detected as similar to an FFA or Link Farm by some other search algorithms, so could cause a severe loss of ranking in those engines.