For me the must-haves are:
- A bike
- A rack & pannier
- A spare tube, and a pump, because even though it's only four and a quarter miles, that's farther than I would care to walk at the end of the day.
- A helmet.
- A tail light.
Optional items that I prefer to have with me:
- A headlight. I never commute (to or from work) after dark but its flasher mode makes me more visible.
- A bike computer because I like to keep track of mileage.
- Gloves
- Change of clothes.
In the winter I also mount fenders, but I remove them as the weather becomes more reliable.
I also use the bike for trips to the store, which can happen after dark. In those cases the front and rear light become mandatory, and my bottle blinky (side light) is the optional accessory that I much prefer having, for safety's sake. I do carry a multi-tool that I never need.
A lock would be on my list, but I leave mine at work.
I am a fair weather commuter. If it's raining I take the car to the light rail station. If it's clear, I take the bike.