In addition to the NASA missions used in research for space weather (see 2020 Heliophysics Fleet) there are additional missions operated by NOAA used for space weather forecasting. As of spring 2020, here's a tour of the NASA and NOAA Heliophysics fleets from the near-Earth satellites out to the inner solar system.
The satellite orbits are color coded for their observing program:
Magenta: TIM (Thermosphere, Ionosphere, Mesosphere) observations
This visualization presents orbits of the current heliophysics satellites covering the space near Earth, out to the Sun-Earth Lagrange point, L1, and finally a view of the current missions operating in the inner solar system.
Hinode: Observes the Sun in multiple wavelengths up to x-rays. SVS page
TIMED: Studies the upper layers (40-110 miles up) of Earth's atmosphere. SVS page
ICON: Works with GOLD on studies of the ionosphere.