The New 3DS has two options: MicroSD Management (built-in to System Settings) or FTPd.
MicroSD Management works best on Windows, since it uses Microsoft's SMB protocol to communicate with the computer, but OS X and Linux does have some good support for this protocol too.
FTPd (formerly ftBRONY) was made by mtheall, was forked from smea's ftPONY I believe. It can be installed as a CIA, and can be used if you're more comfortable with FTP clients like FileZilla.