I would consider the .380acp to be the absolute minimum caliber you should carry for self defense. I would not consider it to be an effective duty use caliber as it lacks the ability to effectively penetrate FBI testing protocol barriers such as windshields, sheet steel, and appendages prior to impacting the torso or head.
The .380acp does just fine when it comes to penetration if you use good ole hardball(FMJ) ammunition. This is why Wild Bill's .36 caliber revolver was able to be effective in addition to his outstanding marksmanship. However, when using hollow point ammunition you need to be very selective. The .380 90-95gr bullets have very low sectional density, which means that they have very low momentum behind them relative to their bullet diameter. So, they are fairly weak penetrators and when you add the parachute effect of a hollow point you get marginal penetration. A lot of hollow point .380s don't meet the minimum penetration depth in testing gel of 12". There are a few that do, such as the Hornady 90gr XTP and the Speer Gold Dot 90gr JHP.
Like all calibers, shot placement is the primary prerequisite of handgun wounding effectiveness, but the other important part of the equation is that the ammunition must penetrate deeply enough to hit the large blood bearing organs of the body. In 1986 special agent Jerry Dove had perfect shot placement on gunman Michael Platt, however his 9mm Winchester Silvertip did not penetrate deeply enough to kill Platt. That same round had an average testing penetration of 11" in ballistic gel.
http://en.wikipedia.org/wiki/1986_FBI_Miami_shootout
Here's a good quote by Urey Patrick at Quantico many years ago on shot placement and the importance of good penetration and expansion and it still rings true:
"Shot placement is obviously critical, and our test criteria presume that the shot is placed in the vital area of the body, which contains the brain, upper spinal cord, heart and aorta/vena cava. This area runs from just above the eyes to the diaphragm, and is about 4 inches wide. But, as our experience in Miami amply illustrates, shot placement is only the first part of the equation. Jerry Dove placed his shot perfectly(he was using a P226 9mm with 115gr Winchester Silver Tips). Bullet performance is critical to translate shot placement into an effective, incapacitating wound. If shot placement was all that mattered, we could arm all Agents with .22's. Secondly, perfect shot placement may be difficult to attain in the stress and dynamics of a shooting incident. The larger calibers offer a "margin of error" in that where a smaller bullet may just miss the aorta, for example, the larger one in the same placement will damage it. A good example is killing a 400 pound pig with a .22, something commonly done on the farm. If the shot placement is exactly right, the pig is instantly killed. If it is off less than an inch, the pig goes wild and the process of killing it becomes rather lengthy and involved, whereas a larger caliber would succeed with a larger margin of miss than an inch.(Larger calibers are not used because they ruin too much of the pig - a consideration that does not come into play in a shooting incident - and besides which, nobody is going to die if the pig is not instantly killed anyway. In shootings, just the opposite is true)."
I would use the .380acp for a CCW, but I would also take into account the penetration limitations of the round. I would choose to use Hornady 90gr XTP JHPs if possible.