There’s a fun, topical, and incredibly difficult mathematical extension of your question: once you know that bubbles seek their minimal surface structures, you might ask what the minimal surface structure of two bubbles stuck together is. We know the answer roughly, of course—just pour out some bubble bath and stick them together. But to get the answer in a mathematically precise way is very difficult; the so called “double bubble” problem was solved only in 2000.
Pictures and explanation of double bubble are available at http://mathworld.wolfram.com/DoubleBubble.html. Here’s a portion of their description:
It had been conjectured that two equal partial spheres sharing a boundary of a flat disk separate two volumes of air using a total surface area that is less than any other boundary. This equal-volume case was proved by Hass et al. (1995), who reduced the problem to a set of 200260 integrals which they carried out on an ordinary PC. Frank Morgan, Michael Hutchings, Manuel Ritoré, and Antonio Ros finally proved the conjecture for arbitrary double bubbles in early 2000. In this case of two unequal partial spheres, Morgan et al. showed that the separating boundary which minimizes total surface area is a portion of a sphere which meets the outer spherical surfaces at dihedral angles of 120 degrees.
This is just another one of those ways in which unbelievably hard problems arise by pushing a little harder on the most innocuous questions.