There are two PDE solvers that I came across recently which look good. Both are FEM based.

Elmer has a good gui and has many physical models already available. There is a good amount of manuals and tutorials available. To get all of them, check out the code from svn. It also has some ability to program your own solvers but this is not well documented. It is a good aid for teaching numerical methods. Windows executable can be downloaded from their website. There is also a Mac binary made by someone else. But for Linux, you will have to compile it yourself.
http://www.csc.fi/english/pages/elmer

deal.ii is a FEM library which is very powerful in the sense that it is a general PDE solver. To use it you have to write your own code using deal.ii libraries. They have the best tutorials I have seen, which takes you step by step from simple problems to more complex ones. It also has discontinuous finite elements. I am currently working through the tutorials. It has very rudimentary grid generation capacity and you will have to use an external grid generator. One limitation of deal.ii is that it supports only quadrilateral/hexahedral elements.
http://www.dealii.org