A bit of both. Hubble can have single exposures that are hundreds of seconds long - but remember it's in low orbit, so eventually the subject will fall beneath the horizon. Most Hubble observations stitch together exposures from multiple orbits. Ultra Deep Field is an extreme example which comprises ~a million seconds of exposure over 400 orbits: https://en.m.wikipedia.org/wiki/Hubble_Ultra-Deep_Field
In astronomy you need multiple exposures to get rid of cosmic rays, which appear as bright lines or dots. A median filter can be applied to the exposures. HST uses tools called drizzlepac and multidrizzle to combine multiple dithered images to better make use of the telescope's native resolution which would otherwise be degraded by the detector.