Where can I download software for modeling magnetic systems?

All in this list are for Magnetostatic solvers - Updated as of February 19, 2019

Free / Student (Limited) versions:
FEMM - FEMM (2D / RS) https://www.femm.info/wiki/HomePage
Integrated Engineering Software - Magneto (2D / RS) https://www.integratedsoft.com/
Tera Analysis - Quickfield (2D / RS) http://www.quickfield.com
Open Source - Poisson / Superfish (2D) http://laacg.lanl.gov/laacg/services/serv_codes.phtml#ps
Mentor-Siemens - MagNet (2D) https://www.mentor.com/products/mechanical/magnet/magnet/

Shareware:
Not aware of any

Professional / Full price:
Mentor-Siemens - MagNet (2D / RS / 3D) https://www.mentor.com/products/mechanical/magnet/magnet/
Ansys - Maxwell (2D / RS / 3D) https://www.ansys.com/products/electronics/ansys-maxwell
Integrated Engineering Software - Magneto (2D / RS) https://www.integratedsoft.com/
Integrated Engineering Software - Amperes (3D) https://www.integratedsoft.com/
Dassault - Opera 2D (2D / RS / 3D) https://operafea.com/
Tera Analysis - Quickfield (2D / RS) http://www.quickfield.com
Altair - Flux (2D / 3D) https://altairhyperworks.com/product/flux

2D = Two dimensional
RS = Rotationally symmetric (Axisymmetric)
3D = Three dimensional

Thanks to UKPete (again) for his suggestion