I can't think of one thing - including the particular bike I ride - that I couldn't commute without. Or, to put it another way, there is no thing that I have needed on every ride.

I really like having a rack on the bike, but I have commuted by backpack.
I wouldn't ride at night without a light, but I would commute in the summer without one.
I always wear my helmet, but I never have used it on the commute.
I always carry tools and tire repair equipment, but I almost never use them.
I carry a garage door opener and use it twice a commute. But it's not essential.
I love my cold and wet weather gear, but I don't use them on warm, dry days.
I love my fenders, but... you get the idea.

I think the thing I value *most* is a tire repair kit and pump. If I were just starting to commute and all I had to ride on was the most basic of bicycles, I'd start by getting a pump, tube, patch kit, gloves, a helmet, and a lock - probably in that order.