OK, there needs to be some clarification here. A bike with a dropout pivot above the dropout is NOT a single pivot, and it does not act like one.

If you look simply, you might think that it is single pivot because the axle rotates on a single path around the main pivot, but what is not being taken into account is shock compression rates. There is a lot more to suspension design than just axle path. 4 bar linkages change the shock compression rate throughout the stroke, allowing the designer to adjust the feel of compression throughout the stroke.

Single pivots drive the shock directly with the swingarm. The difference here is that with a 4-bar, you can work to tune out some of the unwanted suspension action, so they are great for XC and trail, and a single pivot is much smoother throughout the stroke, so better for big hits, but is much harder to tune out unwanted feedback unless you run an SPV or similar shock.

The original statement of this thread is wrong by looking at suspension systems too simply. There is a drastic difference between Horst and 4-bar, namely the dropout alignment which allows for better pedal feedback, and then there is an even larger difference between the two of them and true single pivots.
VPP, DW, Quad Link are all 4-bar systems that have been modified with shorter links. One good thing that came out of Specialized's patent greed is that these systems were able to flourish, while they might not have come out if everyone could have just stolen Horst links without paying Specialized.

here is the list, amended to take into account all aspects of the suspension system.

Trek / Gary Fisher = Fuel/Sugar/EX = Pivotless 4-bar Cake= Single Pivot
Raleigh / Diamondback = 4 bar
Cannondale = Rush/Prophet = Single Pivot Scalpel= pivotless 4 bar
Kona = 4 bar
KHS = 4 bar
Mountain Cycle = Single Pivot
Santa Cruz = Single Pivot (Super Light & Heckler)
Transition = 4 bar
Turner = 4 bar (Pre-2006 = Horst)
Jamis = 4 bar (Pre 2004 = Horst)
Yeti = pivotless 4 bar
Ventana = 4 bar
Devinci = Horst in Canada (in the USA = 4 bar)
Giant = Maestro-4 bar NRS-Horst AC-4 bar
Ellsworth = Horst (Except Isis, Joker, Distance = Single Pivot)
Iron Horse = DW Link (short 4 bar) (except Yakuza = Single Pivot)
Intense = VPP (short 4-bar)
Mongoose / GT = Single pivot with floating BB
Norco = Horst
Specialized = Horst
Santa Cruz = VPP (all short 4-bar) (Blur, Nomad, VP Free, V10 (I think)
Titus = Horst
Rocky Mountain = ETSX (ETSX is a Horst with an elevated chainstay) (Others = Single Pivot)
Marin = short 4-bar

By patent, a Horst is a 4 bar link where the dropout is an integral part of the seatstay. The ETSX is very close to violating the Horst patent, and if you wanted to stretch, most of the short link 4 bar systems have the dropout as an integral part of the seatstay, so they could go that far, but it would be a hard one.

Now, it was said that the 4-bar non-horst bikes were single pivots. Part of the discussion was about braking. Without the actual Horst pivot, it is possible for these bikes to stiffen up and act more like single pivots under hard braking. HOWEVER, it is not simple enough to just call them single pivots because for the rest of the time, they do not act like single pivots.

Also, there was some talk about Single Pivots being easier to maintain. This is not entirely true unless it was designed well. There are more bearings in a 4-bar, but there is less stress on each bearing and thus they will last longer. For instance, my Prophet used two bearings the same size as Ellsworth uses in their Horst bikes. That was the entire pivot. The bike was very wiggy and the bearings went fast. Ellsworth uses a much larger bearing on their single pivot bikes thus the stress is matched with proper amount of bearing. So maintainence is more dependent on proper engineering of the pivots.