Some reasons the Hubble users are such fans include:

It has diffraction-limited resolution, and not just resolution but the whole point-spread function (PSF, what an unresolved star looks like) is very close to the theoretical limit all the way from 110-2200 nm. Below 300 nm the ozone (still) blocks the light on the ground, and adaptive optics (a) work much less well in the visible than the near-IR and (2) give amazingly sharp image cores but substantial and time-variable halos, which take a lot of work to calibrate and (as far as I know) set the precision limit on such applications as quasar host galaxies.

This means that, for example, HST could (with the loss of STIS, that's in the past tense barring a miracle with the next shuttle flight) set its spectrograph aperture 0.3 arcseconds from a quasar core and get a measurement with a small and pre-calculable contribution from the quasar, which AO still can't do. One amazing observation in this vein was measuring the differential Doppler shift from opposite limbs of Betelgeuse to drive its direction of rotation (the bright spot in the HST UV images is around its north pole).

Long uninterrupted viewing windows are a rarity for Hubble, happening only for the piece of sky close to the instantaneous poles of its orbit (which is why Chandtra and XMM-Newton are in such high orbits) - the deep fields were composited from large numbers of single exposures. This advantage of space observations matters only for certain kinds of variable objects where there is an aliasing effect from daily, monthly, or annual interruptions (and this turned out to matter for the key project on Cepheid variables - they could schedule for much more uniform efficiency of detection if the periods of observation need not strobe against the Moon's phases).

Furthermore, the sky background is lower from space than from the ground at all wavelength ranges. This isn't a big deal in green light (the V-band brightness is only twice as high at a good dark site), but becomes more important blueward, and especially into the near-IR, where the gain can be factors of thousands. Thus 10-m telescopes on the ground can outdo HST ony by having 16x tyhe loight grasp plus spending a good deal longer on an observation. (Note that the diffraction limit of HST reaches 0.3 arcseconds at 2200 nm, something which several large telescopes can routinely sneak up on without AO - there is an extensive white paper available from www.stsci.edu detailing the tradeoffs of each approach). This is one driver for JWST and Herschel.

An additional issue is that HST time is allocated from applicants worldwide, and publicly available AO systems have lagged greatly. The only such system available for applications (last I heard, anyway) from any US astronomer is Hokupa'a on Gemini-N, while Keck is available to applicants from UC, Caltech, UH, and NASA-supported work on planetary systems (plus any sufficiently close collaborators, etc.). ESO has done a better job, with high-quality systems tested on their 3.6m and implemented at the VLT. (This also means that astronomers in the cultural outback have more trouble keeping up with the capabilities of AO systems). None of this is meant to belittle the enormous technical achievements in AO, by the way - my nominee for "coolest thing ever done at Keck" would have to be Andrea Ghez' group measuring the orbits of stars around the Galactic Center and basically nailing the case for a massive black hole (work which was largely confirmed at almost the same time by Genzel's group using the VLT).