It probably depends. At the beginning of the year (my 1L year), the ethics director of my state bar gave a talk to my class and was asked a similar question. In this case, the concerned student committed a DUI 5 years ago, I think. The ethics director responded--and the dean of students agreed--that so long as it was your first and only transgression--and, most importantly, that you disclose it fully for the bar AND on your law school application--you needn't worry about reprecussions re not being admitted to the bar.
One caveat was voiced, though: if the transgression was a a violent felony or misdemeanor, or possession of pounds and pounds of a controlled substance, all bets are off.
But, assuming your act with the requisite honesty, the bar (in New Jersey, anyway) will most likely ignore any "youthful indiscretions," to use my dean's phrase.