More than the wearer (owner?) of the tattoos is comfortable with is too many. It's a case by case thing. It depends on the individual, how they dress and where the tattoos are (if you have full sleeves but can cover them with a business shirt if you need to it's a non issue) as well as what they do for a living or plan to do. If you plan on working in a very conservative field it's probably best not to have visible tattoos, though that is slowly changing.
I knew a sixteen year old who had eight tattoos and I thought she'd gotten too many too quickly given her age. Never mind that it's illegal for under eighteens, I could maybe see some people being mature enough to choose a tattoo they wouldn't regret at that age, but eight is rushing things more than a little, especially if you just choose designs from flash without much thought as to what it means instead of getting something that is actually important to you personally.