The components inside are quite vulnerable to static shock, which is why (if you order a part like RAM or a new drive) they ship them in little anti-static baggies. However, the computer itself usually has a grounded metal casing that shields those fragile components from that kind of damage.
If you scooted your chair across the floor and zapped your computer I wouldn't be really concerned. If you were installing your new motherboard or something like that, and zapped it, then I would be very concerned.
It may have been more of a problem a few years ago. I've been tinkering inside PCs since I was 12. I was a part-time PC repair technician during college. I often serviced PCs while they were running, even had a few electric shocks. Too my knowlege I've never damaged any components with static charge. That's not to say it does not or will never happen.