The simple answer is NO. There are many SEO myths out there and this is one of them. There is a popular belief that backlinks from .gov and .edu sites carry more weight than other top level domains. Google have made it clear that they do not (see this interview; and this video – around 4min 20sec into it). There are many SEO Kiddies who go after these links and there are many who sell link pakages with .edu links in them.
Many universities and schools let students set up their own private web pages in the .edu domain, so links from them are so easy to get, so why should any search engine give any more weight to this link than any other not on a .edu top level domain (TLD)?
The spammers have also made sure that the .edu links carry no more weight. See this search result for viagra site:edu – why would the search engines want to give an extra .edu boost to these links?!
Having said that, links from web sites that have good domain trust and really are true authority sites will theoretically be more valuable. Most of the .edu sites will be recognized as authority sites, but not because of the .edu domain name, but because of their backlink profile. Conversely, many .edu sites will not be recognized as authority sites because of their backlink profile.
In addition to the video clip linked to above, there is this more recent one, in which Matt Cutts says the same thing: