Here's a list of known VNC flavors:

Original AT&T VNC

RealVNC

UltraVNC

TightVNC

EchoVNC

Windows-only:
eSVNC
ZVNC
LapLinkVNC
xVNC
Cayote VNC

MacOS:
OSXvnc
OS9vnc
ChromiVNC
VNCThing
CoTVNC

Linux and Other:

DirectVNC
Windows CE VNC server
PalmVNC 2.0
VNCViewer for PocketPC
SmartVNC for Microsoft Smartphone OS
SSHVnc
tkvnc
TridiaVNC

This is the original VNC application, used as a starting point for other variations. It is still hosted here, though the available download is kept current with what's available from RealVNC.

Generally speaking, all other flavors of VNC are compared against this one, to determine if those flavors are "fully compatible" or not.

EchoVNC is a full-featured version of VNC based on UltraVNC
with echoWare integration. 

With EchoVNC on both sides of a connection, two VNC users 
can connect to each other regardless of firewall or router 
configuration. VNC becomes "firewall friendly" -- no more 
port-forwarding!

EchoVNC uses the same EchoWare software that Kaboodle
uses. It is free, Windows-only, fully compatible with all flavors 
of VNC, and of course open-source. You can find it here:

            http://echovnc.sf.net

Note: EchoVNC is a product of Echogent Systems, Inc., which 
      hosts this VNC FAQ-O-Matic website.

eSVNC, or "Easy VNC" is a relative newcomer, but is very popular due to its great featureset. It is based on TightVNC 1.2.2, supports file-transfers, Server-Side Scaling (SSS), and includes some great speed enhancements. You can find it here. It's available only for Windows and, except for the special features mentioned above, is fully compatable with RealVNC.

The eSVNC developer has recently transitioned his efforts over to UltraVNC. So it is unclear if eSVNC is still being actively developped.

ZVNC is an experimental derivitave of two open source projects: VNC and 
ZeBeDee, a utility to set up encrypted, compressed tunneling between two 
hosts. It is possible to use ZeBeDee with VNC without using ZVNC, but 
doing so requires additional configuration of both client and server, and
inherently is less effecient and more prone to error than using VNC alone. 

ZVNC integrates encryption and compression into VNC, while remaining compatible
with both ordinary VNC and with configurations where VNC and ZeBeDee were used 
in combination.  Perhaps surprisingly, the compression component of the
combination is a significant improvement over VNC alone. 

Download the Binary distribution here, Windows only: 

               http://home.attbi.com/~davedyer/znc/zvnc.html

LapLinkVNC is a version of VNC which has integrated SSL support into 
the Windows VNC server and the Java Applet viewer.

The binary is available here:

https://www.mylaplink.com/html/s/public/client/laplinkVNC.exe

The source is linked from here:

http://www.laplink.com/products/lle/rc.asp

Note:  It will run standalone, however, it will generate a self-signed
certificate for the SSL session unless you provide it with a real
certificate.  The self-signed certificates will generate warnings
from your browser and the applet viewer requires a check box to be
checked in order to accept them. Just point a web-browser to
"https://servername:5800" and it connects.

xVNC is a Windows application that combines a remote-installer and a VNC
system all in one. With it, you can remotely install VNC onto a target 
machine and immediately connect to it. xVNC is, by default, deinstalled when 
you disconnect. Access is restricted, of course, to domain administrators.
If you're looking for a quick, unobtrusive way to VNC into to a Windows 
computer that doesn't have VNC installed, this is it.

Windows-only, open-source. You can get a copy here:

http://xvnc.sourceforge.net/

From the release notes:

This is mostly a bug fixed, performance improved, WinVNC version 3.3.6.
There are no major feature changes, and only one minor feature change.  As a
concession to useability, code for keeping the local client viewer open and
automatically resized upon changing the remote server screen resolution was
migrated from eSVNC/UltraVNC into this code.  Otherwise, the entire feature
set of WinVNC version 3.3.6 has remained unchanged.  I would have liked to
include TightVNC's local cursor handling, but that would have broken the VNC
viewers on other platforms.

Windows only, open-source. You can get it here:

binaries: http://www.coyoterd.com/WinVNC-336-patched-exe.zip
source: http://www.coyoterd.com/WinVNC-336-patched-src.zip

OSXvnc is, simply, a full-featured VNC server for Mac OS X. 

It's open-source and MacOS X only. You can get a copy here:

http://www.redstonesoftware.com/vnc/

OS9vnc is a full-featured VNC server for Mac OS9, based on
based on ChromiVNC from Jonathan Morton, and brought to you 
by the same people behind OSXvnc.

It's open-source and MacOS 9.x only. You can get a copy here:

http://www.redstonesoftware.com/vnc/

ChromiVNC is an implementation of a VNC Server which runs on Macintosh. 
It works well with the VNCThing VNC Viewer.

You can get it here: http://www.chromatix.uklinux.net/vnc/index.html

If you'd like the Drag Manager to work with this flavor of VNC, 
be sure to install vncpatches68k:

http://amcg.th.ic.ac.uk/~adrian/vnc/

These patches are needed by ChromicVNC on both 68k and PPC if 
you want the Drag  Manager to work.

Thanks to Lex Ein for the info!

VNCThing is a really good Viewer for the MacOS (8.x,9.x,OS-X).
It's fully compatable with the RealVNC server, it's free, and
it's open-source. You can get it here:

           http://www.webthing.net/vncthing/

"Chicken of the VNC", or CoTVNC, is simply a VNC Viewer for MacOS X. 
It includes speed optimizations, customizeable CPU throttling for the
frontmost and other connections, a manual Refresh command, and 
Tight encoding. It's a good compliment to OSXvnc, a MacOS X 
VNC Server.

It's open-source and MacOS-X only. You can get a copy here:

http://sourceforge.net/projects/cotvnc/

DirectVNC is a variant of a VNC Viewer specifically for Linux systems. 
Unlike other VNC flavors for Linux, DirectVNC takes advantage of the 
"linux framebuffer device", via the DirectFB library. This means that 
the VNC Viewer no longer needs to have a full-fledged X-server installed. 
Instead, the Viewer device can be running the relatively tiny DirectFB 
library: http://www.directfb.org, making DirectVNC suitable for 
deployment on small-footprint think-clients and embedded Linux platforms 
such as LEAF: http://leaf.sourceforge.net.

You can download a copy of DirectVNC here: 

            http://www.adam-lilienthal.de/directvnc/

This is a "bare bones" VNC server for Windows CE. Currently only 
uncompressed encodings are supported. It has been ported from the 
Original AT&T WinVNC version 3.3.3.r9 as part of a feasibility 
research project.

Open-source, find it here: http://sourceforge.net/projects/wincevncsvr/

PalmVNC is a VNC Viewer the Palm OS platform. It should work with
every standard VNC Server.

You can get it here: http://palmvnc2.free.fr/

From its website:

I have compiled the VNC client for the PocketPC by adapting the WinCE 2.x 
source. This is my first attempt to make the user interface PocketPC friendly, 
so it may still have some issues. This download is completely free, and is
available in ARM/Xscale, MIPS, and SH3 binaries. Please note this ONLY works 
on PocketPC devices. To install, copy the correct vncview.exe for your cpu 
type to the device. To uninstall, delete the vncview.exe on the device. 
Note: The Intel Xscale PXA250 (ARM) processor is supported. 

You can get it here: http://www.cs.utah.edu/~midgley/wince/vnc.html

SmartVNC is a VNC Viewer for Microsoft's Smartphone OS.

You can get it here: http://www.centacto.com/smartvnc.php

SSHVnc is a VNC viewer, written in Java, that combines the TightVNC
Viewer with an SSH client. With this app, you can login to your
target PC's SSH server and VNC Server at the same time, thereby
saving yourself one step in securing the VNC connection.

More info available here: http://3sp.com/products/sshtools/sshvnc/sshvnc-features.php

Thanks to gregb at ifost.org.au for the pointer:

There is a pure Tcl/Tk viewer as part of tcllib:

http://cvs.sourceforge.net/viewcvs.py/tcllib/tclapps/apps/tkvnc/tkvnc.tcl

It is convenient if you want to have a VNC viewer embedded inside another
application which supports TCL scripting.