Ignore LOCIS. I think it's been dead for years.
Generally, you want:
http://cocatalog.loc.govfor anything after 1978. Everything prior (well, almost) is found in the Catalog of Copyright Entries. Mark Ockerbloom maintains a set of scans of the renewal pages at:
http://onlinebooks.library.upenn.edu/cce/It was originally intended for Project Gutenberg researchers, I believe, but access is access. Mark also maintains a couple of indices, including links to OCRed versions of the documents, first renewals in periodical series, and so forth. And you don't need to remember the URL, since it's the first search result on Google.
If the pages you want aren't there (for example, you want to find the original registration, rather than the renewal, or are interested in a movie rather than a book or magazine), or just want to see things in context, scans of the full books are starting to appear on Google Books, and it's very likely that your local library has been sitting on a set in the basement.
A word of warning, though: The Copyright Office has always been staffed by human beings, and as such, things fall through the cracks. Clerks may have accidentally renewed works that weren't eligible, misfiled a valid renewal, or failed to type the entry into the catalog. So, if you're protecting business interests when you're checking that Strange Fantasy issue, it's probably well worth the money to hire someone in the DC area to investigate the original documents. Notarized copies of the pages where something fails to appear and affidavits will presumably last a bit longer in court than "b-but I saw it on the web."