Pros
I was able to grow into a career in software development, thanks to in-house and on the job training and opportunities. The size of the company affords a great benefits package, with tuition reimbursement, and a variety of health plans, 401 K etc. Because the company has so many different areas of business, employees can gain experience in different business units via internal transfers, and grow their career within Fidelity. Different areas almost have different business "personalities." The company also welcomes back any "alumni" who had left on good terms. There is a commitment to excellence and integrity to their customers.
Cons
You will never work so hard! Underachievers need not apply. If you don't like change, don't work at Fidelity! (however, some people enjoy change, so this is a pro, not a con!) Business units reorganize, individual jobs transform. Depending upon the business unit you work in, there may be lots of bureaucracy or it may resemble a start up - this is why Fidelity is hard to generalize about.