I'm currently preparing an essay on the Semantic Web as part of my MSc. studies with Open University, so it's a subject I'm particularly interesting in, and in some ways it was actually my interest in the Semantic Web that finally got me to set up a blog. Why?
As such, we do need the Semantic Web. Every time we link in an RSS/Atom feed to a page, or adds a FOAF profile to a page, we're building the Semantic Web.
Longer term, the work on ontologies and schema languages such as RDF Schema and OWL promises to bring a lot more advanced features, such as reasoning about data to allow agents to "understand" new data types and integrate data types using new vocabularies automatically into their data models.
However, short term, whenever the scripts you use to maintain your blog autodiscovers trackback info, or you fire up your RSS reader, you are seeing the early fruits.
As for benefits, consider this: Bloggers are currently dealing with older RSS, RSS 2 and Atom, all of which have different vocabularies.
One of the most immediate benefits of the Semantic Web is unifying vocabularies. Instead of asking for the author of a feed, you'll use a library to query for a specific concept so that when somebody releases YetAnotherFeedFormat v1, and it's RDF linking to an OWL schema, your software would automatically know that your "author" concept matches YetAnotherFeedFormat's "SomeDudeWhoWroteAnEntry" tag, except that the latter also includes "CoolNickName", and would be able to use the data from the new format without having to release a new version.