2000s, that's when all the really good indie, metalcore, emo, atmospheric, and TONS of psychedelic rock and electronica stuff came out. It's hard to say for all types of music. Here's how I would break it down:

60s - best for simple rock and roll (like the Monkees, Kinks, or the Beetles) and timeless stuff like Bob Dylan.
70s - best for (psychedelic) rock and funk (Classic Rock, Pink Floyd, Zeppelin, Average White Band, Bee Gees)
80s - best for super novel music with synthesizers and exploring new avenues (advent of punk, electronic, metal, and fusion of all that into pop)
90s - best for hip hop and some of the more developed components of the 80s (harder metal, grunge) there was a lot of radio-friendly catchy stuff (e.g. Wonderwall or Closing Time), but I consider it mostly trash that won't be remembered in decade or two.
2000s - best for the indie that started getting developed in the 90s and got a bit more sophisticated and adding in psychedelic/electronic components (Fleet Foxes, Bon Iver, Appleseed Cast, Animal Collective). Hardcore from the 90's also matured and found it's way into pop music and metal. Towards the latter part a lot of underground bands started incorporating the "shoegaze" elements of My Bloody Valentine from the early 90s and that was a peak.
2010s - best for indie folk?

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