Just how many outlets do you need for your stereo?

You need as many outlets as are required to plug in all your gear.

Another question to consider is, how many amps are required to effectively power your gear?

Finally, does it really matter whether you plug digital gear into a different outlet from your  analog gear when both lines go back to the same place?  Some advocate running the entire system off of one line.  Is one 20 amp line enough, 30 amps? 

Good point @spatialking. I use three separate 20A circuits (one for each monoblock and one for front end gear) and do maintain some level of filtering on the digital side, using an Isoclean unit.  However, the quote below from the VH Audio site indicates the filtering protects the gear from grunge on the mains, although I suspect the filtering will also protect analog from digital as long as the analog gear is not plugged into the same side of the filter as the digital gear:

For the perfectionist, the IsoClean 60A3 II is fitted with two ultra low impedance Audio Grade 60+60 AMP RF noise filters to attenuate noise and RF associated with city mains. The dual filters of the 60A3 are separate and independent of each other, in order to reduce interactions between your system's components.

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.