The PuTTY executables and source code are distributed under the MIT licence, which is similar in effect to the BSD licence. (This licence is Open Source certified and complies with the Debian Free Software Guidelines.)
The precise licence text, as given in the About box and in the file LICENCE in the source distribution, is as follows:
PuTTY is copyright 1997-2021 Simon Tatham.
Portions copyright Robert de Bath, Joris van Rantwijk, Delian Delchev, Andreas Schultz, Jeroen Massar, Wez Furlong, Nicolas Barry, Justin Bradford, Ben Harris, Malcolm Smith, Ahmad Khalifa, Markus Kuhn, Colin Watson, Christopher Staite, Lorenz Diener, Christian Brabandt, Jeff Smith, Pavel Kryukov, Maxim Kuznetsov, Svyatoslav Kuzmich, Nico Williams, Viktor Dukhovni, Josh Dersch, Lars Brinkhoff, and CORE SDI S.A.
Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation files (the "Software"), to deal in the Software without restriction, including without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to permit persons to whom the Software is furnished to do so, subject to the following conditions:
The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software.
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
In particular, anybody (even companies) can use PuTTY without restriction (even for commercial purposes) and owe nothing to us, or to anybody else. Also, apart from having to maintain the copyright notice and the licence text in derivative products, anybody (even companies) can adapt the PuTTY source code into their own programs and products (even commercial products) and owe nothing to us or anybody else. And, of course, there is no warranty and if PuTTY causes you damage you're on your own, so don't use it if you're unhappy with that.
In particular, note that the MIT licence is compatible with the GNU GPL. So if you want to incorporate PuTTY or pieces of PuTTY into a GPL program, there's no problem with that.