Can't in Texas, nor would I if we could. I'm not opposed to it in general, but personally I'd rather not have a target on me for the bad guys. Although it is a very effective deterrent to criminal activity, it also makes you the first to be in their sights should they want to do harm.
Concealed carry is far safer in that regard. I just wish more responsible citizens were eligible... only about 800,000 in all of Texas can even get a CHL.
Revising my position on this. If you live in an area that respects an individual's right to protect themselves without permit restrictions, open carry daily!
Thinking about this subject, and as a responsible sheepdog, you think about certain scenarios. For instance: Should you happen to be in a convenience store where a criminal enters to do whatever they're going to do, whether you are carrying concealed or exposed, your FIRST action is to move for cover or concealment from which you can maintain a level of tactical superiority. Odds are, said douchebag will not bother to imagine that someone might be carrying, nor would they be looking for a gun on anyone's hip... they'll certainly scan for a uniform, but not sidearms. Whether you're carrying concealed or exposed is of no consequence, except perhaps to add a level of inconvenience to getting your firearm at the ready due to being concealed.
Same goes for a restaurant, retail store or just about any other situation.
Exposed carry also has the double benefit of allowing you to interact with your fellow citizens peacefully while carrying a firearm. It might sound corny, but most people are simply uncomfortable with firearms because they are rarely seen in public. After watching the news/tv and movies, most people are programmed to think that if they see a gun, nothing but bad things will happen. Those of us who carry concealed (the only method of carry that Texas allows), and our immediate friends and family, know this is not true. Exposing our neighbors and other locals to the safety factor of law-abiding citizens carrying is paramount to repealing these unconstitutional laws which prohibit the carriage of firearms.