I am a natural left-hander who took up guitar about 3-4 years ago and had the same dilemma. I talked to the folks at the guitar store and searched the web on this question and after much pondering..... I took up the guitar right-handed.
One of the arguments for doing that is if you go to somebody's house and mention that you play guitar (something I still haven't done

) , if they have a guitar it's likely to be right-handed (The usual argument about us lefties adapting to a right-handed world.)
In the beginning, it seems like the left hand is doing the harder work forming the chords. But, of course, if that were truly the case, right-handers would play the guitar the opposite way. As you get into it more, as dennis pointed out, you learn that the "right hand" side is actually the most important for maintaining rhythm.
About a year into playing the guitar, when I thought I was really sucking and not improving, I went to a guitar shop and played around with some left handed guitars and considered switching. But, I didn't switch. I still play right-handed and don't intend to switch back. But, it is an excuse, I use occasionally

for my slow progress. I am doing the best I can, I am just left-handed.
By the way, I took up golf a few years ago and bought left-handed clubs.
Jim