Packing an emergency kit for your vehicle is extremely important. For one, it keeps items you may have had loose in your car ready to access and easy to find. Secondly, having these things on hand in the first place could save your life. Having a bag gets you organized and allows you to keep a detailed inventory in order to appropriately pack what you need.
The bag can be just any bag large enough to hold these items. It should be something durable and appropriate for the size and quantity of the items you intend to pack in them.
The contents I divide similar to how I pack my Bug out Bag. I think about the essential groups. You don't have to pack what I recommend but if you pack some things that satisfy the needed requirement.
1. Maintenance and repair
I keep a small tool set with drivers, sockets, screwdrivers, wrenches and pliers.
I also throw in a pack of assorted fuses. You will be surprised at how often these can get you out of a bad situation. I once got stranded on the lake in my boat for want of a fuse.
It is a good idea to keep a flashlight and or emergency beacon as well in case of breakdowns.
Jumper cables are an ABSOLUTE necessity. Even better is a self-contained charger.
I also include in my vehicles a portable, plug in tire inflator and a couple of bottles of sealant for tire leaks. I also keep a plug kit but even I consider that overkill.
2. Personal Care
A small first aid kit is necessary.
I like to throw in a bottle or two of water and some freeze dried foods. You never know when this might come in handy.
A change of clothes is nice to have in even non-emergency situations.
A blanket is also a good idea to have. Being stranded in a snowstorm when your car will not start will make you glad you kept one in your car.
Maps of areas that you frequent. That doesn't just apply to the state you reside. I keep maps of all states that I could possibly be in. I generally have them on hand anyway so I just pack them in.
Other optional (but worthwhile) ingredients include:
Lists of phone numbers of family members and emergency services (other than 911!)
Extra cell phone batteries/chargers, etc.
More importantly is the skill to use the items you pack. Get training, or have someone help you practice.
Keep in mind, the better you pack the more likely you will be to have life-saving items if the situation calls for it. The bag needs to be in your vehicle at all times. It will not do you any good if its at your house when you break down.