Pros
They are extremely supportive of work/life balance, offering flextime and work at home options. They are a very stable, mature company who treat their employees with respect and courtesy. As a result, they have a freakishly low turnover rate. I used to wonder how they managed to make money with all the employee coddling they do... but they make money hand over fist, year after year.
Cons
Like most tech groups, they are outsourcing a TON of jobs to India. This creates a lot of stress for US-based employees, who struggle with both time differences and culture/language obstacles. Amex goes on a 12-18 month cycle of layoffs, and they seem to be getting deeper and more frequent. People don't often quit the company, but the constant spectre of layoffs feels like a game of Russian roulette sometimes. Because the company is so mature, they have very rigid processes. They're trying to establish an entrepreneurial splinter group to develop mobile applications to stay competitive, and they've deliberately kept it separate from the rest of Technologies so it can function more like a west coast start-up company. However, peeps who are used to the silicon valley atmosphere will HATE Amex unless they get into that one mobile dev group.