CWCom
CW Communicator or CWCom for short is a piece of Windows software which allows hams and non-hams to communicate via CW over the internet, similar to HamSphere but does not require a subscription, CWCom is free to download and use and does not require a licence since it uses the internet.
It is currently maintained by G3MS, an ex RN wireless telegraphist, CWCom can be downloaded from the Internet Archive and more information can be found on G3MS's blog dedicated to CWCom (MorsePower) regarding setup, interfacing a key with your PC, and installing on Linux and Mac OS systems via WINE.
Similar Software
A similar piece of software (though not exactly related to Amateur Radio) using the same codebase is available for American Railroad Morse (landline telegraphy), unlike CWCom it simulates a landline telegraphy circuit and uses the original American or Railroad Morse code instead of the standard International Morse used over Radio. (MorseKOB)
VBand operates similar to CWCom but does not need to be installed, it can be used in the browser.
Morsecode.me is yet another website where users can communicate via CW and without downloading any software.