Just how many outlets do you need for your stereo?

ONLY ONE.

A 15 amp standard house outlet will supply about 1800 watts. To be conservative, say 1500 watts.

This will EASILY cover most amplifiers of up to about 300 watts rms/channel, as well as ALL the other paraphernalia like tt, preamp, dac, streamer, CD player, etc, etc.

It is actually best practice to connect ALL your equipment to the SAME outlet to avoid ground loops.

If you use more than one outlet and their grounds are not at EXACTLY at the same potential (even a tenth of a volt difference is enough), you will have a ground loop and you may not be able to get rid of the hum & buzz, unless you use a ground lifter, which may be illegal in your locale.

Stick to ONE outlet.

@cakyol Actually, all of the equipment is plugged into one outlet.   I agree, everything should run from one potential.   A while back I had one amp plugged into an outlet 6 feet away but it was wired to the opposite side of the distribution panel, so the second outlet was out of phase with the first outlet.   I always had a hum problem until I got a breakout panel of 16 outlets that plug into the first outlet.   The resulting annoyance is what started this thread.   I am going to upgrade and I am trying to decide how many outlets my power conditioner should have for future proofing.   It appears that 20 is plenty based on what everyone has posted, assuming wall warts and fat plugs don't cover up adjacent outlets.  

spatialking,

As long as you are on a single outlet, you can have a walwart extender to plug in those wide annoying boxes :-)  Since the plugs are very close to each other in electrical terms, it is unlikely you will have a ground loop problem.

This one has 10 physically widely spaced out ports for almost everything and rated at full 15 amps.  I think you can connect an entire studio to it :-)

https://www.amazon.com/TESSAN-Mountable-Extension-Security-Safeguard/dp/B07VVKSYCZ/ref=sr_1_8?dchild...

It is a question that cannot possibly be answered. It is dependant on what you own and what you intend to own. You could need anywhere from 4 to 20....who knows?? What is most important is not plugging the power strips/conditioners into different circuit legs. Keep them all plugged into one circuit, preferably a 20 amp dedicated circuit. The niagara 1200 is a great device. Also, the much cheaper furman pst-8. It is designed by the same guy. These two mentioned will give you I believe 15 outlets.
I use both plugged into a single AQ Edison receptacle wired with 12/2 romex (50 ft) to the service panel using a separate 20 amp breaker. Below are a list of what I have plugged into the two...

Integrated amp
Sacd player
Cd transport
Dac
Tuner
Turntable power supply
Phono preamp power supply
Headphone amp power supply
Cassette deck
Digital streamer
Total: 10 items currently...will be introducing my kenwood minidisc recorder and second turntable at some point, so that will be 12 outlets used.....

One circuit may be the optimal way to go, but some who have really powerful amplifiers may want more power than 15 (or even 20) amps for the whole system.  
Also, some don't care for conditioners/filters and would rather plug their gear directly into the wall, particularly analog gear.  If installing new power, having multiple lines should not be a problem if they are dedicated (i.e., directly wired to a single outlet so they do not power anything else) and all run from the same side of the panel.   I believe there may be other best practices such as keeping audio circuits away from circuits powering noisy fans and resistive/variable type devices.  Another option is to establish a sub-panel (like 50 amps) and then run all the audio system outlets from that.  I am fortunate that my 3, dedicated, 20A lines are absolutely quiet.