First, there was a recent post on what people spend a lot of their time doing as bioinformaticians. It was called What Do You Waste Your Time On. You might get some ideas there.
Second, there is a high level of programming ability in the bioinformatics community. So, many are used to just scripting whatever they need. In a lot of cases, the end users of bioinformatics software are other programmers. So many programs never get very much polish because the users can usually hack them into something usable without a lot of handholding. Two addition causes of gaps in available software are that the technology keeps changing, making old software obsolete and necessitating new versions, and that most bioinformaticians work in an academic environment where inventing new things is rewarded and maintaining old things is not. I bring all this up so you can a sense of what the bioinformatics software ecosystem is like since you are thinking of getting involved.
Third, my suggestion for a cool project that would be tremendously helpful and accessible to the beginner is writing a program that can easily translate between a large number of bioinformatics data formats. There are a few programs that do some conversions, but no single program that does the vast majority of conversions between say: bed, bedgraph, fixed wiggle, variable wiggle, bigwig, bigbed, sam, bam, fastq, fasta. This is a tremendous amount of work though.
Wow!!!!!!!!!!!!
My comment was just meant to illustrate the eclectic nature of the field. People that work on RNA structure prediction, high throughput sequencing, databases for system's biology, theoretical aspects, phylogeny etc will use vary different software, there is no software that is a sine qua non for being a bioinformatician.
Ok thanks. I'm new at this, so I was looking for a more concrete answer. But I do understand what you mean. I should have been a bit more specific.