The qualifications depend on what kind of grad school you want to go to and what kind of program. In general, you should have a 3.0 gpa and a decent score on your GRE ( around 600). With that you should be able to get into the graduate department of most universities.
If you want to go to a top tier school ( Harvard, Yale, etc), you need a GRE of near 700 ( pretty damm hard) and a GPA of something over 3.75 as a starting point. You also need great, serious references, an awesome essay, and a great interview. Top tier schools accept around 10% of all applicants.
If you want a professional degree (MBA, Doctor, Lawyer, Pharmacist, Dentist, etc) you have to do well on their prescribed test (GMAT,LSAT,MCAT, etc) as well as have good grades. But there are ways around this. Many colleges will eneter you into their graduate programs on a probabtional basis if you show enough desire ( or will pay enough $). You can also go to school abroad or to many of the degree mills that will churn out a Profesional degree so that you can take the accrediation test.
To be honest, at the graduate level, it is very important what school you go to, especially for MBA programs. The pay diference for a top UT business school grad and a Harvard grad is about $40k in the first year.
If you just want a grad degree, it is really not that hard to get in. It is whether or not it is what you really want to do.