Background
This type of buffer is called "diamond buffer". The name comes from the shape of the circuit and is patented, US patent 3302039, filed in 1964 . The name "Jung Super Buffer" (from his article) has also been seen in the DIY audio comminuty. Many IC's have this diamond buffer, LT1223, BUF634, LME49600 and many more.
This buffer can be used in a preamp as line stage without gain, as a buffer for DAC's and CD-players. You can also use it for driving headphones. The buffer is rather small and very thin so it can be placed in narrow spaces.
There are lot's of good info out there on this subject. Walter Jung has written a couple of good articles and one of them is about this particular buffer. In fact his article is THE best for a normalDIY'er.
Reference articles
Realizing High Performance: Buffers (Part I) (can't be found but I have it.)
Realizing High Performance: Buffers (Part II) (can't be found but I have it.)
The ancient LH0002 is also a simple diamond buffer. The equally ancient LH0033 consists of a JFETbuffer.
AN-47 from Linear is a big document, very well written. Look especially at page 45-47. Those pages describes a discrete diamond buffer.
AN-227 from Texas Instruments is also worth reading.
This Texas document has also a part about diamond buffers.