I find GoodReader to be the best. I consider it as my iOS Finder (by lack of better solutions, sadly).
It supports a wide range of protocols and web services such as AFP, WebDAV, FTP, SFTP, Dropbox, Box.net, Google Docs, SugarSync, IMAP and POP3. It used to support iCloud as well, but the feature is gone for stability and legal reasons.
It also makes it easy to upload an annotated version of a file at the same place you downloaded it.
Oh, and if you want to access all of your Mac files, SFTP is the way to go. Once you activated "Remote login" in the Sharing pane of System Preferences, you can connect via SFTP to your Mac with your username and password. As the server, use the address (something like
My-MacBook.local given in the same Sharing pane (at least on the same local network).