at the most basic level, the only absolutely essential piece of equipment that you need to be a bicycle commuter is a functional bicycle.
as for the accessories, their importance will vary from person to person:
- some will say that racks and panniers are essential, but the backpack commuter might say otherwise.
- some will say that a water bottle and cage are essential, but the commuter only going 3 miles might say otherwise.
- some will say that fenders are essential, but the commuter in phoenix might say otherwise.
- some will say that lights are essential, but the commuter who rides exclusively in daylight might say otherwise.
- some will say that a helmet is essential, but the commuter who doubts the safety of helmet wearing might say otherwise.
- some will say that a good lock(s) is essential, but the commuter who has indoor secure storage at work might say otherwise.
- some will say that a flat repair kit and pump are essential, but the commuter rolling on marathon pluses might be a dice-roller and say otherwise.
in other words, there are no essential accessories in a general sense. individual circumstances and preferences will determine each individual's choices for the commuting accessories they feel they need.
for me, these are my essentials, in order of importance
1. saddle bag with flat repair kit (tube, patches, levers, CO2 pump, multi-tool)
2. helmet
3. lights
4. backpack
5. water bottle and cage