Flint W.’s Answer
This was a concern of mine when I was in college as well, but my worries were squashed the first time I sat in a corporate interview. As long as you don't have any so-called "job stoppers", i.e. neck/face/hand tattoos, you're probably in the clear.
For example, I've got a 4"x7" piece on the back of each arm (tricep area) as well as a large 3"x7" piece on the top of my right forearm, and because I've always worn long sleeves while in the workplace no one has ever been any wiser.
Due to generational differences, it's understandable why those in upper level management positions would look at tattoos in a less than favorable light, and even though times are changing and most people in yours and my generation do indeed have tattoos, that stigma will be there for a bit longer (at least until the boomers have mostly retired, etc.). So, in conclusion, as long as you're not openly exposing the tattoos and/or telling the world about them, I think you'll be fine when it comes to entering the corporate work force.