Never Say You're a Consultant
Most people don't care what your employment status is. As long as you're doing your work and helping others do theirs, they don't care if your an old-timer, new employee, consultant, or intern. So unless asked, don't make your status known. Instead, behave like an employee and you're more likely to be treated like one.
During one contract at a bank, I did such a good job of behaving like an employee that I was nominated for an award. Of course, I wasn't eligible for the award since I was a consultant. However, because the process was initiated, my manager learned of the nomination which, in my mind, is as good an outcome as I could've hoped for. It's always good to have your manager know that the people you're working with are happy with your work. Especially when it comes time to renew a contract or negotiate a rate increase.
I believe in "blending in" with the client's culture, however I believe it should be balanced with the fact that you are an outsider. In addition to not sharing the company perks, such as the award, a consultant should never get too comfortable. Being critical of company policies or employees is unprofessional as an employee, but even worse when a consultant is overheard by client employees - no matter how much they may agree. Also, while employees may be allowed to do personal tasks at work such as paying their bills or going on the internet for personal reasons, consultants should work on only client related tasks while on the client site.