Tube Preamp: How many tubes does it take to .................

Tim de Paravicini's later (and still currently available) EAR-Yoshino pre-amps use far fewer tubes. The 868PL (phono and line) uses two tubes per stage, the 868L (line only) just a pair of 7DJ8's. The 912 uses the same two line stage tubes as the 868, with three tubes for phono gain.

The ARC SP-9 mentioned above by @curiousjim is a tube/FET hybrid design, not a pure tube one. That's why it uses only a single tube for each stage. IMO ARC hybrid pre-amps sound more like FET's than tubes (I've owned two).

My preamp uses one cathode-follower tube in the line stage but has 8 tubes (and 4 MOSFETs) in the power supply. My phono stage has 3 tubes for RIAA and 4 tubes in the power supply. The point is that tube preamps tend to use the most tubes regulating the power rather than amplifying the signal. And where there is a dearth of tubes, there is a reliance on solid stage regulation instead. 

I'll be interested in a thread about Number of tubes in a amplifier.

Be very interested to learn benefits of many tubes in an amplifier, and what they are used for in the sonic chain

Maybe someone has a link to better understand tube use inside an amplifier

My next line stage is going to have 6 power tubes in the signal path.

There are many ways to design pre-amps.  And many different designs can sound good based on execution and taste.

The basic functions of a line stage pre-amp: 
 - Select from multiple sources
 - Support maximum source input voltage (no overload)
 - Control attenuation (most common) and amplification as needed
 - Provide a high enough input impedance to the source to not affect the frequency response or dynamics
 - Deliver enough gain to drive the amplifier to full output
 - Provide a low enough output impedance for the connecting cable and amplifier to not affect the frequency response or dynamics
 - Add minimum noise
 - Add minimum harmonics (a.k.a. "distortion")
 - Minimize phase and timing errors
 - Do not restrict bandwidth

If you prefer a KISS approach, a single ended pre-amp can get by with one triode gain stage per channel.  This could be one dual triode tube, or two single triode tubes.  Tubes by nature have a high input impedance.  If chosen carefully, a simple single triode stage can meet most of the above criteria usually for a short cable and highish impedance (often tube) amplifier.

There are many other approaches.  A design like the classic Dynaco PAS uses feedback as so requires two high gain tubes stages (one tube) per channel.  Some designs use a cathode follower which requires another one or two tubes.  Other designs (like some Conrad Johnson) use many paralleled triodes per channel.  If a pre-amp is fully balanced, then everything is doubled.

As mentioned previously, some pre-amps use tube rectifiers (one shared or one for each channel) and some designs also use tube voltage regulators.

As you add functions and features you can add even more triodes/tubes.  A phono stage adds a minimum two triodes (one tube) per channel but can be more.  Other features requiring more tubes can be a tape loop and phase inverter.

So, depending on performance, features, and convenience requirements/preferences, old and current pre-amps can use few or many tubes.  This variety makes our hobby fun, IMO.