I might be wrong, but I do not think that the primary goal of bioinformatics is to prove that evolution takes place. The question whether evolution did happen/happens/will be happening has been more or less settled before bioinformatics became popular.
Are you perhaps looking for informatics/computer science applications that are related to research in evolution? If so, go to http://www.ncbi.nlm.nih.gov/pubmed and simply search for 'evolution', one of the first results is the paper 'Why do humans have chins? Testing the mechanical significance of modern human symphyseal morphology with finite element analysis.', which uses finite element analysis -- something that can be modelled and simulated very well in software. I am sure you could find more papers related to modelling/simulation if you narrow down your question to a few key points.
Otherwise, the references given here should be sufficient: http://en.wikipedia.org/wiki/Evolution
Of course, if you have a very distinct opinion about evolution to start with, you will find this web-page much more appealing: http://www.conservapedia.com/Evolution
It's important to realise that biological scientists accept evolutionary theory because multiple lines of evidence support it. Some of these stem from bioinformatics analysis, many do not. As Joachim pointed out, we've been addressing these questions for a long time (at least since the 1850s) and a PubMed search will return the results: currently 163 067 articles with the word "evolution" in title/abstract. As to whether evolution is "in progress" this is not a separate issue: the word itself implies an ongoing process.
Having said that, some of the best evidence for evolution comes from what may be called bioinformatics approaches. Identifying the same gene in several species by sequencing it implies that those species share a common ancestor (leaving aside issues of homologs, orthologs and paralogs). Using differences in gene sequence to cluster those species into a phylogenetic tree demonstrates the degree of relatedness. And modelling the rate of change in the gene sequence - molecular clocks - gives an estimate of when species diverged.
Already nice answers, I would like to share my thoughts from the perspective of the protein evolution.
Understanding of evolutionary aspects of proteins are accelerated by several bioinformatics approaches. For example protein sequence classification (protein families, clans, protein domains) and protein structural classification (domain, family, superfamily, folds etc) are two areas where bioinformatics contributed to the understanding of evolution of protein structure and function.
Two popular bioinformatics resources based on such concepts are:
I would like to point you to couple of interesting article about the evolution of protein families across sequence and structure space.
The E. coli long-term evolution experiment is a nice example of real experimental data for ongoing evolution. In this experiment, different E. coli populations are followed for more than 50000 generations, and the appearance and spread of genetic adaptations is shown.