There are 3 multi-gold Medal winners, but for my money, the most impressive is Rebecca Romero
Getting a Silver 4 years ago in Athens in Rowing and then switching to a totally different discipline - i.e. Cycling and getting a Gold this time shows what a true sportsperson is about.
Phelps with his 8 gold medals may be the "greatest" of all time, but how much variety is there there?
4x100m free relay - so 100m crawl
4x200m free relay - so same as above, but bit longer

200m freestyle - so another 200 crawl

100m butterfly - yup, 100m butterfly
4x100m medley relay - another 100m butterfly

200m butterfly - same again, bit longer

200m medley - 50 metre each of crawl, butterfly, breaststroke and backstroke
400m medley - as above, but bit longer

so a great achievement for sure, but only got 8 medals as there are so many on offer compared to loads of other sports.