Seems this thread is computer systems/network heavy so I'll add a little bit for those more inclined to programming
Anything with databases...PERIOD. The larger companies, whether they be brick-and-mortar or online, rely heavily on databases for a huge portion of their internal operations. For my part I work in data warehousing/Business Intelligence, which is currently a hot field and has been for the last 10 years or so.
Definition of Business Intelligence
Business intelligence - Wikipedia, the free encyclopedia
To get started, learn some object-oriented programming like Java or C# (C++ would work too) and also relational database concepts. Those are core competencies for data warehousing and should only take a year or two of serious study. Once that's out of the way, you can often find data warehouse/business intelligence courses in universities, community colleges or vocational IT schools.
Admittedly, this line of work typically requires a bachelor's degree and isn't easy to crack into like networking or systems administration (or even straight programming like Java) but once you're in, you're golden. I fell into this line of work by happy chance right out of school and started at $42k/yr...within three years my pay jumped to $82k, nearly double. After 5+ years experience it's not atypical to make $100k/yr which I'm nearly at now.
Anyone interested in this line of work can find more information on job responsibilities and skillsets on Monster.com or Dice.com. Just look for the keywords data warehouses, business intelligence, and/or etl.
Or you can ask me