Pros
The pay is competative, there are opportunities for international travel or assignments, the company is very stable. Being an integrated oil company there are a very wide variety of job opportunities. Engineers, lawyers, doctors and nurses, pilots, oil field workers, ranch managers. No matter what your profession, the job likely exists in ExxonMobil. Exxon is one of the last large companied to have both a savings plan and a defined benefits plan for retirement. This is a benefit that should not be underestimated for people that are looking for a long term career. The employees that Exxon hires are typically very competent so your coworkers are very good to work with.
Cons
The atmosphere is "command and control". Information about your career is on a need-to-know basis and you don't need to know. The words "...up to and including termination" are used continuously in connection with relatively minor infractions of rules. The HR leaders have no clue how to create a corporate environment where people want to work for the company. The Mobil side of ExxonMobil was lightyears ahead in this aspect but the merger seems to have gone completely with the Exxon style in this area. The company is actively working to move jobs to low cost centers in other countries. If your job can be done from any site then it's only a matter of time before it is moved to a place where someone will do it for a fraction of the typical US saleries.