There seems to be quite a lot of interest right now in companies trying to build platforms for cloud-based 'genetic-analysis-as-a-service', such as DNAnexus. The data management/storage and scaling problems in genomics are very real, but to a large extent these issues are not really specific to bioinformatics. There are also companies working on software for NGS, such as Real Time Genomics and Novocraft.
Historically, pure-play bioinformatics startups have had a pretty tough time, perhaps because the primary users have been academics who are loathe to pay for software. I think many of the successful ones also involve proprietary databases (eg. Ingenuity) or have deep scientific experience and expertise (eg. OpenEye).
The real opportunities at the moment are more likely in companies that are tightly integrating genomics technologies with diagnostics and services. There are many, but for example, look at Foundation Medicine in cancer, or Counsyl or Natera in prenatal diagnostics.