Source code of Tesseract's Releases.
Binaries for Linux
Tesseract is included in most Linux distributions.
Binaries for Windows
Downloads Archive on SourceForge. There you can find, among other files, Windows installer for the old version 3.02.
Currently, there is no official Windows installer for newer versions.
3rd party Windows exe's/installer
Cygwin includes packages for Tesseract.
binaries compiled by @egorpugin (ref issue # 209) https://www.dropbox.com/s/8t54mz39i58qslh/tesseract-3.05.00dev-win32-vc19.zip?dl=1
You have to install VC2015 x86 redist from microsoft.com in order to run them. Leptonica is built with all libs except for libjp2k.
https://github.com/UB-Mannheim/tesseract/wiki (installers available for version 3 and 4)