Physical Danger
It's unlikely that you'll deal with much physical danger. Computer guys and gals aren't generally known for adventuring or risk-taking or even going outside regularly. On-the-job injuries are typically limited to accidentally jabbing your hand with a screwdriver and things like that.
So unless you're the network admin for a chain of MMA studios, and you happen to also be really bad at your job, you should be okay.
Of course, sitting a lot, hunching over screens, and squinting at tiny type can have long-term effects. But, like any office worker, you can help stave off those problems by hopping on the treadmill and cutting back on the Chips Ahoy.