Staying prepared is key to avoiding catastrophe and is one of the major reasons you should always have a roadside emergency kit. Aside from the standard supplies like a spare tire kit and jumper cables, you should always keep extra supplies to help you in any circumstance.
According to the DMV, you should carry a first aid kit at all times. This should be stocked with things like gauze and bandages, medical tape, antibiotic ointment, over-the-counter painkillers, vinyl gloves, tweezers, scissors, and cotton balls.
You should also consider taking some basic tools. This includes a Phillips head screwdriver, a flat head screwdriver, adjustable pliers, needle-nose pliers, and a roll or two of duct tape. You should be able to slow, if not stop, minor leaks or other issues with this basic tool kit.
Spare fluids are vital for any emergency kit. Water is great for drinking and as a spare coolant. You should also have a spare quart of oil, transmission fluid, and brake fluid as well. If you are travelling somewhere especially cold, consider bringing antifreeze/coolant as opposed to just water.
Other supplies include the following: work gloves, blankets, flashlights, flares, and a pocketknife. Tire sealing kits such as Fix-a-Flat are also great in a pinch, though they are not designed for long term repairs. These are just some of the basic supplies to pack. Be sure to resupply every few months, and feel free to substitute materials based on your specific needs.