Wikipedia tells me that 11 states have permitless carry as of the start of this year. Those states are, Alaska, Arizona, Arkansas, Idaho (residents only), Kansas, Maine, Mississippi, Missouri, Vermont, West Virginia, and Wyoming (residents only). There is an argument that resident only permitless carry does not count, and there is an argument that a resident only condition will not hold up to judicial scrutiny. Regardless of this we seem to be off to a good start.
I've seen news of bills submitted for permitless carry in state legislatures in New Hampshire, North Dakota, South Dakota, Minnesota, and Iowa. With Iowa this change is a bit different as it is currently being proposed as a constitutional amendment, which makes this a longer and more complex process. If I understand the process correctly a constitutional amendment in Iowa must pass in two consecutive legislatures and then appear on a general election ballot. If the people vote in favor then it's part of the state constitution.
I intend to update this thread periodically through the year as state legislatures debate these bills. I'd appreciate comments, contributions of bill status in the various state legislatures, and corrections as the year progresses. With so many states considering permitless carry legislation I expect this list of states with permitless carry to grow.