At the finish line
In two trips the most successful climbers I have seen are long distance runners. These are not necessarily those who have been running a lot lately but those who have run marathons or done a lot of cross country in high school and college. This leads me to believe that there are two unsurprising components to fitness and success - aptitude and training. The absence of one can be made up for by the other, to a point. Some people simply don't do well at altitude and others are virtually unaffected. On my 2005 trip, the strongest climber (named Andre) didn't have a single headache, or any loss in appetite. Two years past he managed to run a marathon in just over 3 hours, after only 12 weeks of serious training. He hadn't been running vigorously leading up to the trip.
My training for my second attempt at Aconcagua consisted of building up very gradually to longer and longer runs. I started in August running about 2.5 flat miles, three times a week. In January 2005 I managed one 10 mile flat run. My pace was relatively slow. For his marathon, Andre did "pyramid" speed training which is alternating short sprints with regular pace running, building up to longer sprints over a set of 5 sprints, then cooling down to shorter sprints.
My training for my third attempt consisted of preparing for a marathon. I ran the California International Marathon Dec 4, 2005. This was my first marathon. I tried to follow their suggested training schedule for first time marathoners. This made a huge difference. In previous attempts I had been at the back of the pack of climbers. In 2006 I was at the front.
So, the moral of this story is train hard, much harder than you think is necessary. The more you train before the trip, the more enjoyable it will be. Beware on the other hand of over training. Make sure you're not pushing it so much that you get injured and can't train or climb. It's also wise to taper off your training just before the trip. Marathon training advice I've read suggests not to run a marathon closer than a month from your competitive marathon, or to run more than a 10 mile run the week before. That probably holds true for mountaineering. People without proven aerobic talent or high altitude experience will need to train harder.