Slightly tangential: When it comes to the aesthetics of the output, the main advantage of the more technical tools recommended in other answers, over Excel and similar programs, is that they have better defaults. It is possible to create good-looking charts with Excel, LibreOffice, etc., if you know all of the things you need to tweak. In order to learn what those things are, I recommend these books:
- The Visual Display of Quantitative Information, E. Tufte (the sequels are also useful, but not as much)
- Data Visualization: A Practical Introduction, K. Healy
- The Grammar of Graphics, L. Wilkinson
- Preparing Scientific Illustrations, M. Briscoe (thanks @henning).
Reading these books will also help you get the most out of something like gnuplot or ggplot2.