Hubble, Chandra, XMM-Newton, Kepler,... I can name a few off of the top of my head, but how many space telescopes are there in all?
More than 20 if the Wikipedia's List of Space Telescopes is accurate. I extracted the active ones, and removed duplicates (to the best of my knowledge):
- Swift Gamma Ray Burst Explorer
- Insight (Chinese: 慧眼)
- Спектр-РГ (Spektr-RG)
- The famous Hubble Space Telescope, HST, see hst
- Lunar-based ultraviolet telescope
- TESS, see tess
- CHEOPS, see cheops
- Chandra, see chandra
- XMM Newton, see xmm-newton
- NICER (Mounted on the ISS).
Interestingly, the majority is satellite based, but there is e.g. also a moon-based one.
In addition to that, there are space crafts whose Instruments have been temporarily or permanently been repurposed to astronomy. For instance, you could look at the Moon with METEOSAT.