My Percheron mare goes in a Myler single-jointed Dee. She's soft and responsive in that bit and it gives her a lot of tongue relief.
Excel and Molly (eventer and dressage horse) both go in single-jointed or french link eggbutts, but I use french links more because it seems that they prefer them just a bit more.
Arthur, my Paso, goes in an Imus easy-gait comfort bit. I LOVE this bit. Tons of tongue relief, a comfy copper roller, and an extra training ring should I need to school with a snaffle action.
My 4 y/o reining colt is in a single-jointed loose ring. He seems to like the nutcracker action.
My reining Arabian goes in a medium port, medium shank correction bit. Her training is impeccable and she responds to all seat and leg cues with a very soft touch on the bridle if need be.