From "Japanese Warships of WWII" by A. J. Watts (the book is improbably sitting on my desk at work...)
-Asahi: old pre-dread or AC, converted to sub salvage/repair/training ship in 1922.
-Akashi: purpose-built repair ship, laid down in 1937. 9,000 t, 19 kts, three large cranes shown in a crude line drawing. No details on capabilities. Four other units were proposed but cancelled.
-Six merchant ships converted to repair ships, no details available.
I recall the Brits converted one of their CVLs to a repair ship while building. I think it was HMS Unicorn. What she repaired, and how well she did it, I can't say right now.
-www.german-navy.de does provide some info on German units that Stephan alludes to.
-http://www.history.navy.mil/danfs/v2/vestal.htm is a lengthy account of what all the USS Vestal did during WW2. Pretty impressive list of things that she could and did do.
http://www.history.navy.mil/danfs/m8/medusa-ii.htm for USS Medusa.
http://www.history.navy.mil/danfs/v4/vulcan-iii.htm for USS Vulcan.
http://www.history.navy.mil/danfs/a8/amphion-ii.htm for USS Amphion