Beginning in the early 1980s, I started writing a FORTRAN program to compute data relevant to the structure of generalized (aka parabolic) Verma modules associated to a finite-dimensional complex semisimple Lie algebra. It is based on the computation of Kazhdan-Lusztig polynomials. A simplified version of the program, called gvm, is available. You will need a FORTRAN compiler (such as f77) to make this work; I have only tested it in a UNIX environment. If you download and use the program, I'd appreciate your sending me an email letting me know.
In Summer 2004, several graduate students in the UGA VIGRE Algebra Group wrote a GAP program to determine support varieties of induced modules for exceptional groups over bad primes. (It is a companion to the paper "Support varieties for Weyl modules over bad primes," University of Georgia VIGRE Algebra Group, J. Algebra 292 (2005), 65-99.) It is available in gzipped tar or zip format.
If you want to do some basic Lie theoretic computations, you can try the online version of the program LiE.
The Atlas of Lie Groups and Representations is a project to make available information about representations of semisimple Lie groups over real and p-adic fields. It is particularly focused on the problem of the unitary dual: classifying all of the irreducible unitary representations of a given Lie group. There is a web interface to the Atlas software.