All the allopathic medical schools in the US are prestigious from a global vantage point-- we have the best medical schools in the world. Period. So objectively the quality of medical education in the US is second to none. Being accepted to ANY allopathic med school in the US is something to be proud of, because it's a privilege afforded to a select minority in the US (just 15,000 people every year).
However, there is a correlation between the ranking of medical schools in the US and the strength of residency matching. Some people would attribute the incredible match lists at places like WashU to the quality of the student body--i.e., that highly prestigious institutions are self-selecting and, therefore, a strong match list is inevitable. However, even the most prestigious institutions (top ten let's say) have class ranking and grading systems in place. At WashU, for instance, the last three years are graded and the class is broken up into three parts for ranking (top third, middle third, and bottom third). Yet, practically every single match for the 2003 graduating class at WashU is awesome; thus, even the people in the bottom third matched well.
My point, then, is that prestige reduces the importance of class rank in residency matching. A really strong institutional reputation can compensate for a "bottom third" class ranking. Do you think that a bottom third graduate of say KU School of Medicine (an unranked medical school) could match into Stanford, WashU, or Northwestern for internal medicine? No freakin way.
World-renowned physicians tend to be faculty members at prestigious schools, which means that you can get letters of recommendation from well-known people in certain specialties--these recommendations can open doors for residency. The stronger the department, generally speaking, the better the graduates match in this field. For instance, WashU students do ridiculously well when it comes to matching into radiology, which is a very competitive field nowadays. It's not a mere coincidence that the Mallinckrodt Institute of Radiology, arguably the best radiology department in the world, is affiliated with WashU.
A similar phenomenon can be seen at UMich with ENT; Michigan has one of the finest ENT departments in the country, and not coincidentally graduates of Michigan consistently match into the very best residency programs for ENT (which is VERY competitive).
More prestigious institutions also offer a lot more research opportunities.
Yet, I can't help but think that patients really don't care about where their doctors attended medical school. The only thing that really matters is how well doctors care for their patients. Fortunately, every medical school produces altruistic, compassionate, and highly competent physicians.
And one last thing...medicine kicks ass!