Pros
Google has a really strong reputation and is a word leader in internet technology. Working at Google opens a lot of doors for later employment externally and also gives you a lot of insight into what it's like to work for a large company that is still in a growth phase. Google also hires very intelligent, hardworking individuals, so you meet a lot of amazing people and work with them every day. It also provides great benefits (health, dental, etc.), and a lot of really nice perks (free food, gym, special guests/events). It's also a good first place to work in Silicon Valley because you learn a lot very quickly about the Valley's culture from an established organization.
Cons
The downsides of working at Google depend largely on the department that you're dealing with. The sales organization is highly disorganized and has a glut of middle management. Management and structure are obviously necessary in all companies, but the sales org at Google has too many managers, many of whom are ill-qualified to be managing other people. There are also a lot of politics surrounding promotions, etc. because of this large middle management structure. It also causes a lot of unnecessary bureaucracy which slows down work and can be extremely frustrating for individuals who are still on the lower rungs of the ladder. Additionally, at least within the sales org, there appears to be virtually no real career path or hope for development/promotion. Managers are hired from outside (with MBAs being strongly preferred), which is frustrating and demoralizing for employees who have worked for years without being moved up.