Honestly it wasn't even a movie that got me into them, it was the TV Show "American Crime Story" on the OJ Simpson trial. I loved learning about the technicalities of trials and the way the show portrayed the characters.
Movies that I've watched that I've liked
A Few Good Men
12 Angry Men
The Trial of Chicago 7
Primal Fear
A Time to Kill
Philadelphia
The Lincoln Lawyer
I've also watched The Rainmaker and Anatomy of a Murder, both of which I just couldn't enjoy.