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 and which will be updated. I use (C) to designate closed-source commercial projects.
Astrophysics
MAS (Magnetohydrodynamic Algorithm outside a Sphere): Model of the Solar Corona and Inner Heliosphere
Climate
Earth System Modeling Framework (mix of Fortran 95 and C++)
MITGCM (general circulation model)
NOAA-GFDL Flexible Modeling System
Computational Fluid Dynamics
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
Materials Science
DAMASK (DĂĽsseldorf Advanced Material Simulation Kit): unified multi-physics crystal plasticity simulation package
Engineering
ABAQUS – Finite Element Analysis for Mechanical Engineering and Civil Engineering (C)
Quantum Chemistry and Electronic Structure
NWChem: Open Source High-Performance Computational Chemistry
SIESTA (Spanish Initiative for Electronic Simulations with Thousands of Atoms)
VASP (Vienna Ab initio Simulation Package)
Wannier90: Maximally-Localised Generalised Wannier Functions Code
YAMBO: first-principles methods based on Green’s function theory to describe excited-state properties of realistic materials
Weather Prediction
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.