1) it must be a novel sequence
2) you must specify the gene product
3) you must specify the product function
The last two points are key, as they prevent the massive patenting of sequences and sitting on the rights until somebody else comes up with a practical application (see: submarine patents).
Interestingly, ESTs and SNPs can also be patented which means there is the potential for multiple patents on the same sequence. Whole organisms can also be patented, provided they are not naturally occurring (GM corn, for example), as can naturally occurring substances, as long as a novel use can be specified.
Currently an estimated 20% of human genes have been patented, but fortunately the government reserves the right to override patents in cases where it is deemed vital for the public good and the patent holder is being overly restrictive. For example, the American Medical Association has asked for a ban on patents for medical and surgical procedures, or, closer to home, the Ontario government ignored a US patent on a cancer screen and offered the test to the public. Similarly, the BC government complied and stopped, but has since resumed offering the test.