The answer is that we support all Microsoft Windows versions from Windows Vista/2008 and higher for x86 and x64 systems. Windows 2008 32 bit edition unless "r2" is also not supported. On Windows 2008 (non-"r2") 64 bit edtion with Servicepack 2, SQLyog 64 bit will run, but SQLyog 32 bit will not.
Support for Windows versions before Windows 2000 (9x, ME) was stopped from SQLyog version 6, for Win2K from SQLyog version 9 and for WinXP/2003/2008 32 bit with the release of SQLyog version 13.
The reason for discontinuing support for old Windows versions, the last two times has happened with releases of SQLyog versions 9 and 13, was solely due to an upgrade of the Visual Studio compiler, we use. Programs compiled with a specific Visual Studio version will typically not run on Windows versions more than 8-10 years older than the compiler.
Also note that old Windows Operating Systems for mobile devices (the various 'flavours' of Windows CE, Windows Mobile Phone 7 etc.) are not supported either. So is also not "Windows RT" Windows version (for handheld devices and some very small laptops) typically running on an ARM hardware architecture.
We also support Wine on Linux and various Unix's (including Mac OS-X). With Wine here may be some 'flaws' and 'quirks' depending on the Linux distribution/Unix type and the Wine version used. But with recent Wine versions and Linux distribution issues are mostly cosmetical. From SQLyog version 13 the Wine version must be 2.0 or higher