Water: Water is the first and foremost important need in the world, which is obvious you need to have emergency water. The amount of water that you need is depended on the amount of people in your family. (or any group of people, like roommates, friends, etc.) Also, the temperature of water does not matter, when you are in an emergency it's best to be hydrated with what you have.
Canned Food: Why canned food? Canned food is packaged to eat, and the main thing is that it is portable. Along with the need of thirst, humans also have the need of hunger. Food supplies us with satisfaction as well as energy to keep us going through the day. To bring food, you must have it packaged and ready to eat (heat may be required) So why not canned food! Take along plenty of these, (also depending on the amount in your group)
First Aid Kit: When a large disaster strikes, there may be people who will get sick or injured during the disaster. First aid kit's are excellent for minor or mild damages to a human. F.A.K's are usually supplied with bandages, creams, and medicines. You can purchase a first aid kit from a certain store (pharmacies, conveniences, and more) or create your own first aid kit at home. One F.A.K should be good enough as long it is packed with everything necessary.
Sleeping Bags/Tents: If there is or is not a shelter for you to take refuge, sleeping bags and tents should be necessary either way. Sleep is a way to revive your energy (but don't forget to drink and eat) If you're going to equip yourselves with tents or sleeping bags, first you must find flat ground. Make sure it is in a safe area (do not sit on the side of a mountain, or under any fallen building that could fall and crush you eventually.) In one emergency kit, it's best to keep one of these with you. (Sleeping bag or Tent)
Matches/Lighters: Lighters and matches will provide you with the same thing, heat and fire. They could be useful to heat up your canned food, or to keep yourself and others warm. To do so, you should learn to build a fire pit and use a match/lighter to start it up. After you've got even a spark of a flame, you won't need to keep lighting it. Try to build it up yourself with paper, dry grass, sticks, or anything flammable. Also blowing onto your baby flame will also be helpful, because fire also needs oxygen to stay alive. Reminder: that blowing with too much force could put out the fire. It is recommended to get waterproof matches, so in any condition it will last. Because of it's size, you should easily carry around one or two handfuls of matches or lighters.
Light Source: The time that you live through the horrible disaster is unpredictable. So when the sun starts to set, a light source should be very helpful to get around, or just to see anything. Flashlights are useful, but to make it even more useful, you should find a solar or wind up flashlight. Solar and Wind Up flashlights require no batteries, and they can last you longer than a battery source flashlight. Although this is mostly a secondary option, you should find those with sirens attached. Solar and Wind Up flashlights can be found with sirens attached, for those times when you need to call out to help (probably a search party or something else) then you can use the siren. It is handy to keep at least two of these light sources with you.
Knife: Knives could be used for multiple reasons. They could be used to open or cut anything that you cannot do with your own hands. Or they can also be used for protection against wild animals or psychotic and starved people. Pocket or Survival knives are very useful, but if you want more than just a blade, Swiss Army knives carry more than just one tool. (A knife can also open your canned food) Usually one knife should be enough for an emergency kit, but to have that extra one just in case is not an issue.
Rope: Ropes are usually looked past, but they are very useful. Bring along rope to keep your belongings together (not necessarily) or if you need to climb up anything steep. Rope's major role is usually for support. Paracord are the most recommended type of rope, because they are very sturdy. (They are also seen in forms of bracelets, for more portability.) Although the rope is heavy, at least 300ft. of it should be good.
Batteries: Batteries are just another tool, (not entirely necessarily). But if you have items that require batteries, it is completely best to have extra batteries. (If you did not get the solar or wind up flashlight, then batteries are necessary if you have a flashlight that uses batteries.) In most other cases, you should also have a portable radio. Also, in where batteries come in handy.
Flare Gun: In my opinion, an earthquake situation wouldn't need a flare gun. Flare guns are usually needed when you are stranded on an island or such. Flare guns are used to attract attention, usually to call for a sign of help. (If a search party, or emergency services need to find you) Remember: Flare guns are limited to how many flares you can use.