When did the Hi-Fi sound mature?

For sheer sound quality on any level, the biggest step from puberty to adulthood was supposed to be the CD player, but now it seems that puberty was maturity as the ultimate in sound seems to still be the turntable?

The definitive greatest step forward was absolutely the electronics of the golden age off HI FI. bewteen 1955 and 1965. Before 1955 or there about everything was mono.
Stereo took root from the late 50s through the mid 60s. The amps were in general low powered except the few that didn't rely on a variant of the EL-84. These amps also didn't make tons of deep shake your guts bass but had a very sophisticated input or preamp section. By the time 965 rolled around Solid State was widely used providing much more power but the amps sounded very flat and dull.
The ultimate advancement in Amp Gismos had peaked with the late 1970s Japanese solid state amps and giant all in one reievers. The best quality amongst them were the luxury brands such as Accuphase and Luxman .
The speakers that were used with the circa 1960 tube integrated amps were very efficient. The Corner Horn by Klipsch the JBL Hartsfeld 1957, The JBL 075 aluminum /alloy compression horn, with a phase plug "bullet tweeter" came out a year or two before that and the D-130 extended range 15 inch woofer with a passive radiating plate for a dust cover making some midrange were all developed by the mid 50s.
The D-130 stayed in production for 40+ years and the Bullet tweeter has yet to be discontinued. Paul Wilbur Klipsch built his horn speaker in 1948 and James Martini AKA B Lansing developed his D-130 driver that same year. The landmark in speakers that set the speaker industry racing forward was introduced 20 years earlier with a coaxial design by Guy Fountain in 1928. The speaker is simply called the Tannoy Black. They were all very efficient taking aim at using the low output amplifier signals that were the norm for that time and providing less tiney more full sounding "Concert Hall" music at realistic volumes.

Whether or not that represent a system that sounds like one made in 2009 is really not the question. Of course it doesn't but getting to this point was always a matter of quantum leaps. Thus it was the big steps that happened which culminated, so far anyway, in SOTA audio.
I for one liked the freedom that all those amplifier controls gave you. Despite the fundamentally poor sound.
I freely admit my volume and source selector preamp only. My current tube power amps with speakers made here and France are sound more to my liking than the low definition that typified the clouded sound of the mid fi from the peak of the imported SS amp/receiver.
I still hope however, that people will pull those plugs out of their ears, and we return someday to everyone having audio played out loud.
There was a time when almost everbody owned and played a stereo, believe it or not.

That's a very generic question. Does it really matter?

Fact is there are more choices to make more people happy today than ever, plus sites like this make good sound more affordable to more people who might care than ever.

I would say that other than better and more efficient amp designs (class D) and expansion in sources and means of delivery of digital music, there is not too much radically new or significant happening in audio design these days in terms of just better sound.

I suppose overall, speaker and perhaps amp designs are more refined and detailed sounding as a whole, but I consider this more refinements to an already fairly mature set of products.

An exception could be products that rely more on digital processing for better sound, like the Emerald Physics line.

The advances in digital since 2004 makes everything before virtually obsolete in my opinion, so I'd say around 2003/04
for decent CD playback(getting near as satisfying as good analogue).

I think this is really fascinating. Putting a finer set of points on the discussion:

1. When did quality "HiFi" first enter people's homes in reasonable numbers?

2. When did "HiFi" or full spectrum recordings become widely available?

3. When did turntable and cartridge technology achieve a moderate level of accuracy in speed, noise level and frequency range?

4. When did Solid State amplifiers finally become recognized as competitive with tube amps in terms of "HiFi" reproduction?

5. When did digital reproduction start to close in on analog in terms of that "you are there" essence (or has it in your mind)?

Interesting that I can't think of a more recent watershed in speaker design to rival the comments above about the early horns and large dynamic drivers. There are so many variations on the solution to this electro-mechanical problem at the heart of music reproduction, that it seems difficult to identify when we "closed in" on where we are now. Maybe when quad introduced the first ESL speakers?

Clearly, the Internet and the iPod have expanded the availability of, and exposure to all kinds of music to people - but also the MP3 has lowered expectations of how music should sound. I submit that the next breaking point in HiFi will come when bytes become so cheap and downloads so fast that iTunes "Plus" will mean true hi resolution bit rate/sample rates, 192 kHz/24-bit, rivaling analogue and far surpassing red book CDs. The only limitation on quality of reproduction will be in the gear used, not the format.

The forces of mass production and mass markets will drive down the cost of higher quality reproduction, whether it is for your head phones, your iPod dock, or your "home entertainment center". As marketers take advantage of higher quality source material, people will begin to expect and demand gear that can keep up with Apple's or Audio Engine's latest thing, or whoever is first to market with the most convenient and exciting "hi-res" gadget.

The next big thing is HiFi is probably not going to come from the hi end, but rather from the mainstream, and we will take it up and push the limits of what's possible.