For processing data files and creating two-dimensional graphs and plots, there is on Linux — to my knowledge — no real alternative to using the ancient gnuplot program.
This is unfortunate, because although I don't want to knock a free program that, in the end, I used quite successfully, I must confess I don't really like gnuplot at all. It does what it needs to do, but its interface is hopelessly old-school and clunky (and I'm not just saying that because it is a command-line interface) and its documentation is a disaster. Every step of the way I felt I had to fight against the program in order to get it to do what I wanted, rather than that it was helping me to achieve that goal.
There are a number of scripts and filters in my thesis sources that I used to beat gnuplot into submission. We are talking ugly hacks here, and my own documentation is hardly something to write home about either, but they may nevertheless serve as a starting point if you need one.
It's been brought to my attention that there may be a possible alternative for gnuplot in the Gri Graphing Language. I have no personal experience with it, but a cursory glance through the documentation would certainly suggest that it might be worth looking into for anybody who is in need of a scientific graphing program.
Another recommendation I received in email is for the GLE Graphics Layout Engine. Again, I am not familiar with this free software tool and am just passing along the suggestion.
And yet another recommendation for a free software graphing environment I have not used myself: the R Project for Statistical Computing.