Although corned beef is traditionally made with brisket (from the chest of the cow) other cuts can be corned. Brisket works well because it's flat and thin, the grain is going the right direction for thin slicing, has no gristle, and although it's pretty tough, it isn't quite as tough as chuck or round from the shoulder. I don't know what you guys call it but here we have bottom round roast - one of the cheaper cuts of beef. That could be easily sliced in half (with the grain) and then corned. London broil (top round) could be brined as well but the grain might be tricky to cut.
Although I mentioned brined turkey as a reference point, I am hugely critical of brining fowl. A lot of our TV chefs push it and everyone jumps on the bandwagon. It involves soaking a turkey in a salt solution for an extended period of time, usually overnight. The solution is soaked up by the bird along with spices/aromatics resulting in a moister, more flavorful turkey. Unfortunately salt has a nasty habit of denaturing protein. In other words, by soaking it in brine you're precooking your turkey resulting in tougher meat. Moister, more flavorful, tougher meat

Brining works well for corned beef because it's a tough cut of meat to begin with and by the time you stew it for hours on end, the toughening effects of brining are completely eradicated.