gnuplot and xmgr/grace are probably the oldest Unix scientific graphing programs. I still use gnuplot from time to time (BTW it is not GNU and some consider it not free), because I know it and I've been using it for many years, but it hasn't changed much in this century and it's not user-friendly according to today's standards.
I think that the most promising programs now are QtiPlot, LabPlot and Veusz.
The first two are similar to Origin (the most popular plotting software on Windows). QtiPlot has a full-time developer and it seems to be developed more actively. Veusz is different than Origin clones and unlike other programs it is written in Python. It's not in the distro yet, but it has PPA.
Another program that I use for plotting data is fityk. It is specialized in curve fitting and I use it for plotting mostly because I know it well (I wrote it), but I guess in most of cases QtiPlot or Veusz will be the best choice.