How many space telescopes are currently active? 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?
Related

What are the next planned space telescopes?
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
AGILE
FGST
IKAROS
NuSTAR
Astrosat
Insight (Chinese: 慧眼)
Спектр-РГ (Spektr-RG)
The famous Hubble Space Telescope, HST, see hst
STSat-1
IRIS
Hisaki
Lunar-based ultraviolet telescope
BRITE
NEOSSat
TESS, see tess
CHEOPS, see cheops
Odin
IBEX
AMS-02
DMPE
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.