Triple bubble conjecture: Natural candidate? 
Is there a standard natural candidate surface for
  the shape that encloses three given volumes
  in $\mathbb{R}^3$ and has minimal surface area?

I know the planar triple bubble conjecture was proved
by Wacharin Wichiramala in 2004 in a paper that I cannot access now
("Proof of the planar triple bubble conjecture." Journal fur die Reine und Angewandte Mathematik 567 (2004): 1-49).
I am guessing this paper may describe the candidate in $\mathbb{R}^3$.
Perhaps "the" is already incorrect, in that there may be several candidate surfaces?
If so, the question could be narrowed to three equal volumes.
Ultimately I am seeking an image of the candidate(s), but any help here would be
appreciated—Thanks!

Thanks for everyone's help!
(I posted this summary at the same time j.c. was
providing his comprehensive answer.)
Here is an image made by John Sullivan:
"a standard cluster of three bubbles, where the surfaces are spherical. Any three desired volumes can be achieved by a Möbius transformation of this cluster":

 
 
 
 


And here is a photograph found at this link:

 
 
 
 


(Added 9Mar14) j.c. found the original photo of the above and noticed it actually has
a tiny 4th bubble!

 
 
 
 

 A: Problem 2 in the list of open problems that Douglas Zare linked to answers the question (namely that there is a standard candidate, and it is even called the standard triple bubble).  
I quote it here with a few interspersed comments of my own.

Problem 2 (Sullivan) We construct the standard clusters of k bubbles in $\mathbb{R}^n$ ($k\leq n+1$) as follows. Start with a regular k-simplex in $S^{k-1}$, and lift this to $S^n$ along longitudes. Then consider different stereographic projections of this complex into Euclidean space; they have $S^{n-k}$ symmetry.

[The following is an image of the standard triple bubble in $\mathbb{R}^3$ as in Lucia's answer. It is by John Sullivan and it is on this page of his website.]


Conj. For any k prescribed volumes, there is a unique standard k-bubble with those volumes

[Here is a copy of the paper by Montesinos proving existence (a result of Brakke's) and uniqueness of the standard clusters (Conj. 1). I am hosting a copy in my dropbox since it seems International Press has removed their online copy.]

Conj. This standard k-bubble is uniquely area minimizing.

[As far as I know this is still open aside from the triple bubble case in the plane (Wichiramala (I'll host the paper for now)) and the double bubble case for $\mathbb{R}^n$ for all $n$ (Reichhardt and another proof by Lawlor).]

Conj. For n=3, these are the only strictly stable k-bubbles ($k\leq 4$). Here we allow bubbles with disconnected regions; strictly stable means that the second variation is positive definite.

[This paper of Morgan and Wichiramala proves that double bubbles (and two single bubbles) in 2D are the only stable bubbles with fixed area. See also this paper of Cicalese, Leonardi and Maggi.]

Conj. There is a strictly stable cluster of six bubbles with a non-spherical interface, but no such cluster has fewer bubbles.  ...

[I include an image from the same page of Sullivan's as above.].

A: The triple bubble conjecture has now been solved in dimensions at least 3.
