Pros
I've been with Chevron for 20 years. Never thought I'd stay anywhere that long, but the benefits/pay/9-80 work schedule are hard to beat. Senior management really seems to listen to the concerns and/or wishes of employees and positive changes are made as a result, e.g., a "bonus" program was implemented a few years back. As oil companies go, Chevron really does care about its people and the communities where we do business.
Cons
If you're not an engineer or MBA, your career ascent may not go as quickly as you'd like. As with any huge company, nothing ever happens quickly. There is always a lot of churn and review processes are cumbersome, to say the least. Many of the middle managers I've encountered in my career are not well equipped to be supervisors. It's frustrating that so many people have spent their entire careers at Corporate and still have no idea what a platform is, what a refinery does, etc.