Savings vs. Investments
First, you need to understand the difference between savings and investments. Savings are funds that need to be available for your liquidity needs. They are what you will need for short-term expenses in the next couple of years, or they are your emergency funds. This money should be set aside in short-term vehicles, such as CDs and money market funds. Investments are funds that you won't need for a while. They can go into longer-range vehicles, such as mutual funds, stocks, bonds and real estate.
It is prudent to plan for unanticipated events. Things happen. Jobs end. People get sick. Children may come along unexpectedly. For those times, it is important to have a little extra money set aside. Or maybe more than a little.
How Much Is Enough?
The general financial planning rule is to have three to six months of your expenses set aside for emergencies. Your "expenses" are how much it would cost you to live if you lost all your sources of income. Figure out what a bare-bones, no-frills budget would be.
This is a general rule. How much you personally need depends on your own particular situation. For investment vehicles that will provide you with liquidity, you should consider money market funds, CDs, and savings bonds. You should also be aware of what you can do in an emergency when your liquid assets just aren't enough.