There is a tremendous amount of work going on in the computational topology community, so this page will be out of date shortly (and already misses plenty). Thus, this page is meant primarily to be a jumping-off point, not a comprehensive list. However, if you'd like me to add something, please let me know, and please don't be offended if you don't see something here -- all omissions are unintentional. 

Things by me  Things by others
  • Eirene (Julia) by Gregory Henselman -Petrusek
  • Ripser-live (browser) and Ripser (C++) by Ulrich Bauer
  • Perseus (C++) by Vidit Nanda
  • CHomP (C++) by Shaun Harker
  • Dionysus and Dionysis 2 (C++) by Dmitriy Morozov
  • Hera (C++) by Michael Kerber, Dmitriy Morozov, and Arnur Nigmetov
  • JavaPlex (Java) by Andrew Tausz, Mikael Vejdemo-Johansson and Henry Adams
  • GHUDI (C++) by Clément Maria, Pawel Dlotko, Vincent Rouvreau, François Godi, Siargey Kachanovich, and David Salinas
  • PHAT (C++) by Ulrich Bauer, Michael Kerber, Jan Reininghaus, Hubert Wagner, and Bryn Keller
  • Topology ToolKit (C++) by Julien Tierny, Guillaume Favelier, Joshua Levine, Charles Gueunet, and Michaël Michaux (I think?)
  • TDA (R) by Brittany T. Fasy, Jisu Kim, Fabrizio Lecci, and Clément Maria
  • TDAMapper (R) by Paul Pearson, Daniel Müellner, and Gurjeet Singh
  • R scripts for TDA (R) by Peter Bubenik
  • Simplicial complexes for Julia (Julia) by Alex Kunin and Vladimir Itskov
  • SimBa and SimPer (C++) by Tamal K Dey,  Fengtao Fan,  Dayu Shi,  and Yusu Wan 
  • Python Mapper (Python) by Daniel Müllner and Aravindakshan Babu
  • Persistence Landscape Toolbox (C++) by Pawel Dlotko​
  • DyNeuSR (Python) by Caleb Geniesse, Manish Saggar, Rafi Ayub, and Jeff Mentch
  • Ripser++ (C++, Python, GPU) by Birkan Gokbag, Ryan DeMilt, and Simon Zhang
  • ripser.py (Python) by Christopher Tralie and Nathaniel Saul
  • BallMapper (R) by Pawel Dlotko
  • flagser (C++) by Daniel Lütgehetmann
  • giotto-tda (C++, Python) by Umberto Lupo, Julian Burella Pérez, and Wojciech Reise (I believe - there may be more)
  • Keppler Mapper (Python) by Hendrik Jacob van Veen, Nathaniel Saul, David Eargle, and Sam Mangham (this is a guess based on their paper)