They provide more career progression opportunities than smaller companies.
They are under more scrutiny, and hence, generally have to be more fair than most other entities (not counting government). Their actions will always be potentially subject to the public eye.
They tend to attract talented people. In many smaller companies I've observed, there are only a trusted few who are really the thinkers and leaders. Larger companies have more smart people sprinkled through the ranks.
Let's face it, they're more efficient. At least up to the point where the synergies of combining operations outweigh the anergies (a term one of my former bosses used to use). Anergies could include -- unnecessary corporate overhead, inefficient communication, being the target of lawsuits simply because of size, etc.
They probably have more staying power, on average, than smaller private firms, although that point might be debatable.
In general, I'm not so much down on the concept of the large public corporation, just the odd way the interaction between shareholders, board, CEO and senior team has evolved. The lack of trust, respect and loyalty. The rampant scapegoating. The quickness with which we fire, rather than work with people. The measurement of expended hours and personal sacrifice, instead of commitment and contribution. The intolerance toward making errors, confessing errors or learning from errors.
Of course, examining the negatives tends to be more entertaining and more controversial, so I probably won't stop doing it, but just this once I felt the tug of my conscience telling me I needed to be more evenhanded.