Ideally, emergency funds should be large enough to cover up to six months of living expenses. This is because one of the worst emergencies that should happen to you is losing your job. Six months should be enough for you to find another job and get financially stable again.
Emergency funds, as the name suggests, should only be used for emergency situations. You should not think about spending the fund for vacations or to purchase new appliances. To avoid the temptation to use for purposes other than real emergencies, it is wise to set up a separate bank account for your emergency fund. This way, your money is far enough so you cannot spend it immediately.