I realize this is an old thread, but it's worth a revival to balance some of the information posted here.
I'm a veteran. When I first enrolled in law school, I had connected with the other vets in my class by the second week. We all quickly learned who the other vets were, what branch everyone served under, and what MOS (job specialty) everyone held. Wherever life takes a vet, he or she knows who the other vets are. If you did not receive an honorable discharge after your tour of duty, you are not only not in the clique, but you're likely to be ostracized by other vets if they find out you were kicked out. But you know that already. My career began with an interview in a field I knew nothing about. The interviewer had also done a tour in the military and we spent a full hour doing nothing but swapping stories about our time in the service. He hired me on the spot. But if my interviewer had learned that I received less than an honorable discharge, he would have stopped talking about the military immediately, and my interview would have ended on the note that several candidates were being considered. I never would have heard from him again.
You have to seriously F up to get kicked out of the military. This is true even if the discharge was for something fairly innocuous like being gay or getting caught with a little weed, for which they had almost no tolerance when I served. If the Army punts you from its ranks for something that didn't involve moral turpitude or a violent crime, then it was your judgment that failed you more than your conduct. To illustrate, soldiers who want to continue being soldiers do not smoke weed on base or have sex in the barracks with each other. It's too risky. That said, those who in the past were given a general discharge for being gay probably have nothing to worry about, other than the homophobia that they might face anywhere. Attitudes have changed. But you'd almost have to walk in the door announcing your sexual preference in order to overcome the blemish of a general discharge. If the discharge was for any other reason except medical, you'll have provide details that are probably very regrettable.
If your interviewer never served, you may be able to conceal your service record. But if your interviewer ever served in any branch, you'll have a difficult hurdle to get over. And given the legal field's interest in an attorney's background, it'll probably be a tough thing to conceal without lying, even if the interviewer never served. Fortunately for you, most people do not serve in the military, so the failure to connect as fellow vets may not matter with every firm that gives you an interview. But a general discharge will matter to some of them, and it will absolutely matter if the firm is run by a veteran.