The fortran-lang site has a paragraph explaining What is Fortran used for? This could be linked to a gallery of production codes with nice external web sites, ideally with eye-catching graphics. Some sites listed below such as ECMWF may not refer to a single computer code. Here is a starting list that I request people add to -- please create a PR or an issue. I use (C) to designate closed-source commercial projects.

MAS (Magnetohydrodynamic Algorithm outside a Sphere): Model of the Solar Corona and Inner Heliosphere

MITGCM (general circulation model)

NOAA-GFDL Flexible Modeling System

CFL3D: structured-grid, cell-centered, upwind-biased, Reynolds-averaged Navier-Stokes (RANS) code, used to support numerous NASA programs since the late 1980s

FUN3D (Fully Unstructured Navier-Stokes): suite of tools actively developed at NASA that benefits Aeronautics, Space Technology, and Exploration by modeling fluid flow

MFC (Multi-Component Flow Code): exascale compressible multiphase and multiphysics flow code

OVERFLOW: uses structured overset grids to simulate fluid flow, and is being used on projects for Aeronautics Research, Science, Space Technology, and Human Exploration Mission Directorates

ABAQUS -- Finite Element Analysis for Mechanical Engineering and Civil Engineering (C)

NWChem: Open Source High-Performance Computational Chemistry

SIESTA (Spanish Initiative for Electronic Simulations with Thousands of Atoms)

Quantum ESPRESSO (opEn Source Package for Research in Electronic Structure, Simulation, and Optimization)

VASP (Vienna Ab initio Simulation Package)

ADCIRC Prediction System -- provides timely, high-resolution information on how coastal storm surge, flooding and winds will impact a [U.S.] coastal community

ECMWF (European Centre for Medium-Range Weather Forecasts)

Global Forecast System (GFS) -- U.S.

Unified Model (UM) -- U.K.