Using RNA-seq to compare gene expression across patients instead of between Control and Experimental conditions
When you say RPKM do you mean crude RPKM or the estimates that you get using expectation maximization methods like cufflinks and eXpress?

It is better if you get your RPKM or FPKM values from one of these programs because you can differentiate between transcript variants.

I have mostly used cufflinks and eXpress. Cufflinks package is better for multiple datasets. You can use cuffquant (which takes SAM/BAM) files to compute FPKM. Cuffquant will also need a reference GTF file. Cuffquant gives a binary .cxb file which you cannot read directly. Once you have generated the .cxb files for all your cohort samples, then pass all these files to cuffnorm. It will normalize the data and give you FPKM values for each gene in each sample in the form of a huge table.

Next point is which genes do you wish to compare. Do you want to compare known oncogenes which show consistent upregulation in all cancers? Actually there is a paper in which they have done this (I'll let you know the reference when I find it. Not able to recollect now).

You can then see how many of these genes show consistent expression in your cohort. Basically you need to identify a set of genes before you go on to study which patient shows anomalous expression.