In my experience, there's always something more you can get beyond the initial offer (why wouldn't try to get you at a discount if they can?). And as your future compensation packages (both at this employer and at future ones) are influenced by where you start, doing what you can to maximize that will pay off handsomely in the long run. The trick is giving them a reason beyond "I want more money" to give you that "something more".
Sometimes that reason can be credentials / experience / skills they're not taking into account (e.g. when I was graduating, one of my offers didn't take my Masters into account), but the best reason is having one (or more) other offers. Having other offers should also give you the confidence to do a better job negotiating. You've probably heard it is best to look for a job when you already have one. One of the reasons for that is that you have a default "other offer". When you don't have that advantage, you have to work harder to create something similar.
Good luck.
Remember to include some examples of why you deserve it--this way, the hiring agent can use the same reasons to make an easy decision.
For example if they offer $60,000 don't counter with $100,000! Most corporations have a budget for each FTE they hire and they almost ALWAYS bring that down by a lot and start the negotiating with that. If the person takes it then good for the corporation and if not, they have some room to get the best price for both parties.
when it's at the point of negotiating a salary, it's almost guaranteed you have the job so just be reasonable and they'll meet you half way. When i was a new grad (5 years ago) they offered me $50K. I countered with $60K. they came back with $55 and based on my performance the first year they would push it to $60 the following year.