First, lets do some simple googe-scence calculations. How big is the main Star Wars galaxy compared to the Milky Way? And is extragalactic travel really possible? According to Starwars.wikia., the galaxy is 120,000 light years wide, whereas the Milky Way (setting of Star Trek) is only 100,000 light years. So therefore even if nobody from either series left their home galaxies but traveled across their own, Star Wars Wins by 20,000 light years.
In the Star Wars series there is the idea that, “somehow there is some kind of “disturbance/turbulence” in the space between galaxies that makes travel between them impossible.” And apart from the few who attempted extragalactic travels never returned. ~ wookieepedia.
Now for the question, did anyone leave their home galaxies? well, the trekkies seem to be at a disagreement about the enterprise leaving the Milky Way. In Star Trek, there are some who remember, “in the original series, The Enterprise was hijacked by an alien couple who altered the ship in some way so that it could break through “The Galactic Barrier” and go to Andromeda. It did break through the barrier, so technically it did leave the galaxy, but Kirk and the crew got control back before it went to the next galaxy.” And also, ” once you leave our galaxy, thoughts become undistinguishable from reality, or some such. :smack:I got the impression it was a matter of leaving the known universe, not just the galaxy. To a region where the laws of physics are different.” ~ Der Trihs & Varlos Z from boards.straightdope.
In conclusion, the nearest galaxy to the Milky Way is the Andromeda galaxy which is 2,500,000 light years away. So in both series they are both quite accurate that extragalactic travel is impossible. So because the Star Wars galaxy is larger, I deam Star Wars the greatest galaxy travelers. Sorry Trekkies.