Free FTP, Secure FTP and Trivial FTP Source Code and Programming Libraries

Copying files via FTP, HTTP, Gopher using Wininet.dll (WDJ Nov 96)
With this library your Windows program can have the capability to get files from the internet using FTP, HTTP and Gopher. Note that this tool relies on Microsoft's wininet.dll which part of Internet Explorer. The actual source code is contained in one of the ZIP files in the archive downloaded (each ZIP file has a README.TXT file that explains its contents).
Putty: Win32 SSH / SFTP Client with Source Code
Putty is not a library, but a set of programs that implement Secure Shell access, Secure FTP (SFTP), Telnet, etc. Since it is open source, employing things like strong authentication and secure sessions, it may be a useful source of information for your own internet software. (You should read their licensing terms before you do that, of course.) Note that the SFTP software is command line driven, so you may not even need to extract the source code for reuse in your programs - you can simply call the command line client from within your own program.
TurboPower Async Professional (FTP, VOIP, etc)
If you need to add speech to your programs, or enable it to process speech input, TurboPower's Async Professional provides you an easy access to Microsoft's Speech API (SAPI) allowing you to integrate voice/speech recognition and speech synthesis in your programs. It also handles the sending and receiving (as well as viewing and printing) of faxes (and converts BMP, DCX, PCX and TIF files automatically), alphanumeric and text (GSM/SMS) paging, high speed file transfers (including the major file transfer protocols like Zmodem and FTP), IP telephony (audio and video, Voice Over IP or VOIP), Internet communications (Winsock access), supports ISDN modems, RS-232 and RS-485 standards, and includes an XML-based modem database. And so on. Like most of the TurboPower tools, this open source toolkit may be used with Borland Delphi and Borland C++ Builder and ActiveX environments like Microsoft Visual C++ and Visual Basic. If you use Borland Kylix on Linux, you might want to try the TurboPower Async Professional CLX version.
War FTP Daemon
The source code for a FTP daemon that can only be used in freeware programs (but not if you are the government, military or any political organisation). You have to fill in a form and the author will inform you where to get the code.
FileZilla Open Source FTP / SFTP Client
FileZilla is a free, open source FTP client for Windows, Linux and Mac OS X distributed under the GNU General Public License. Since the source code for the entire application is available, you can extract the relevant portions for implementation in your program (subject to the necessarily licensing conditions of the GNU GPL).