Carolyn,
There isn't a definitive answer. The answer depends on your lifestyle, your tolerance for risk, you plans for the future.
For instance, lets say you net after taxes $100,000 a year. You live off $40,000. You can save 60% of your income. Since you live off $40,000 a year, when you retire you only need $40,000 in income, so this would be a good scenario to support early retirement, or a high risk job - the type that you are often out of work for long periods of time.
But most of us can't afford early retirement and don't need to worry about only working half time due to a risk laden career.
You should have enough emergency money saved up to support six months of your expenses if you lose a job. That's a good rule of thumb, but may not be necessary if you primary income is a high demand job with low risk (nursing, for instance). If you'd have trouble finding a new job with the same income, you might want a year or more saved up. A person with a high tolerance for risk may choose to save nothing. Someone with a low tolerance will probably feel comfortable having as much as possible set aside.
You should save enough for retirement that you will be able to keep your lifestyle the same - i.e. you income from your retirement accounts, plus spending the principal at a rate equal to your expected lifespan (which is SO easy to predict), should equal your current expenses - minus any expenses you won't have when you are retired (hopefully your mortgage, college, etc, will be paid for before you retire) - but plus any expenses you'll add as part of your retirement lifestyle (travel, golf?).
You should have enough short term savings to cover needing a new washer or new transmission for the car. You don't want the "wear and tear" of life to throw you in sudden debt. However, someone with a low tolerance for risk might save enough to replace the washer, dryer, fix the car and do emergency surgery on the dog, all at the same time. Someone with a high tolerance for risk may feel comfortable with a few hundred dollars set aside.
You should save enough to meet your financial goals - i.e. do you want a new car, save for it. Do you want to finance your kids college (I'm not implying an obligation here, btw), save for it. Are $60,000 weddings paid for by the brides family something you'll be doing, and you have a 14 year old daughter, save for it. In our house we save for college and cars and vacations - we don't save for weddings, boats, snowmobiles.....)