I have a misdemeanor conviction on my record. The charges were for an M1 in my state, underage alcohol possession, but subsequent to a plea agreement I pled no contest to disorderly conduct, an M4. I was honest about it in my application. I tried to show how my experience helped me to mature. I do not believe most schools expect a perfect past from every student. Conviction for a crime through itself does not make you a bad person. What I do think desirable schools are after with respect to a personís character are honesty and integrity. If you can show that a conviction was constructive in your life then I do not believe most admissions offices will want to lord it over you. In fact, I think it might have helped my application as much as it hurt. From what I have seen I expect that I will not have any difficulty being admitted to the bar because of my conviction given that I fully disclosed it to my school at the proper time.
Personally, the arrest and sentence helped to provide perspective in my life on alcohol, school, the law, and societal expectations on individuals.
I am sure the burden on you is going to be different depending on what the conviction is. Felony convictions, I would think, require more evidence from the applicant as to why they can be expected to set a professional legal example in the future. I doubt you can look like a recidivist and be accepted. But I think the idea is the same almost no matter what the conviction; it is more central who you are likely to be in the future than who you probably were in the past. Their view of the latter no doubt comes into play when forming their thoughts on the former, but the two are still distinct. I am also comfortable reasoning that you must accept authority, at least to the extent that if you contest it you do so through sanctioned behavior. Perhaps this description does not fit a good number of those people with criminal convictions. I think it is important to proactively show if it does fit you.
Then again, I have never been on an admissions committee in my life.