Pros
Adobe provides you with the chance to work with well-known, technologically advanced products at a company that, for the most part, truly cares about its employees. You get to work with some very smart and creative people, and the same can be said for many of the customers. Though things may not always be perfect (what is?), it's clear that upper management actively thinks about how decisions affect employees, and continually aims to create a positive work environment with good benefits. It's generally a very open and honest company culture.
Cons
Though the company pays lip service to being customer-focused, and many individual contributors do sweat the details for customers, when push comes to shove customer satisfaction often loses out to short-term profits. That can be frustrating when you're trying to do the right thing. As for work environment, one historical problem with Adobe is that decision-making has generally been very consensus-oriented, which can slow things down. That may be getting better, however. As with any large company, culture and issues will vary a bit based on what department you're in. Some are more political than others, for example, though, in general, Adobe seems less political than most companies of the same size.