Pros
AIG is an excellent place to work if you want to gain experience handling very complicated matters for very high profile accounts from "Day 1". The experience you gain in a couple of years at AIG would take you a decade or more to acquire anywhere else. You have ALOT of freedom in most positions to make your job truly "your job". Overall, the company is a good place to work.
Cons
The downsides are really the flip-sides of each of the best reasons for working for this company. As noted, you gain incredible experience handling very complicated matters for high profile accounts from your first day. The down-side is that you really need to learn alot on your own. There is little training and even less in the way of established procedure and process. The breadth of experience you gain in a short time is impressive, but it can be stressful, too. AIG is so huge that it is easy to feel like a small cog in a giant machine and to lose sight of your role in the overall success of the organization.