The quick answer to this is yes and no. It can be legal if you do it correctly. As long as syndication permission has been given by the content creator, you should by fine. Normally press release feeds, some news feeds, article directories and a few RSS feeds will allow this. Many blogs do not give you this permission though. Also, many that allow syndication will ask for you to provide credit and a link back to their site. The key to finding out if it is legal for you to autoblog is to make sure you know all the places your content is coming from and what their rules are. With most autoblogging software, you do not have this option as they just find RSS feeds and articles from all over that are related to your keywords. This does not make it easy for you stay on the legal side.
Besides legalities, you also may get yourself blacklisted from the search engines. Google is not very pleased with you downloading and reposting the content to build a blog full of adsense content. This is exactly what your doing with autoblogging. If you do a search on Google for autoblogging, you will find forums where people are asking about autoblogging and how much money they can make with it. On top of that, all sites that sell autoblogging software talk only about how you can make thousands for doing nothing all day. This is exactly the reason why Google does not like it. It is duplicated content being posted solely for the purpose to fool search hits into your site for profit.