VNC viewer not connecting to Mac from Windows
I'm not sure which VNC server you have running on your Mac, but you can use the built-in one.
Apple menu --> System Preferences --> Sharing --> Screen Sharing
Make sure that its configured for VNC access with a password. Then try to connect to TCP port 5900 with a VNC client on your PC.
To answer the other question: VNC is the Mac answer to RDP, actually. Even the commercial "Apple Remote Desktop" package ultimately uses the VNC protocol.
I ran this command and could get it to work with RealVNC Open/Free edition viewer. Ensure that on the client, the color level is set to Full [Options->Colour & Encoding->Colour Level]
sudo /System/Library/CoreServices/RemoteManagement/ARDAgent.app/Contents/Resources/kickstart -activate -configure -access -off -restart -agent -privs -all -allowAccessFor -allUsers -clientopts -setvncpw -vncpw secret -setvnclegacy -vnclegacy yes
This method works via the command line (local terminal and remote ssh session too).
Try turning off encryption, works for me for a similar problem.
A few years later, the "world has changed", so
The free version of RealVNC (v. 6.17.1113, Nov 2017, x64) works smoothly for me. In particular from Windows 7 Professional to OS X Yosemite (10.11) and to OS X High Sierra (10.13 w/ latest updates), the "OS X Authentication" that Mac OS builtin VNC requires, with username and password and no tweaks to the VNC server side, posed no problem. These are security types 30 and 35: see https://vncdotool.readthedocs.io/en/0.8.0/rfbproto.html#security
Although performance was clearly lacking. It's using ZRLE compression; perhaps JPEG or something else is superior, and perhaps professional RealVNC is optimized.
TightVNC and TigerVNC both fail complaining those are unknown codes.
[And do everything over a VPN for heaven's sake if going through the Internet.]
Try TightVNC to connect. It seems to work when the free edition of RealVNC does not. http://www.tightvnc.com/
I've also found that the VNC viewer will konk out when connecting to the Mac if the viewer is not running in millions or full color mode.