If you would like to increase the interest received on your money, then holding a portfolio of value stocks or an index ETF will outperform your bank account by a large margin over time. This takes very little effort, but will suffer from the occasional (large) drawdown that you have to sit out or this strategy won't work.
If your primary objective is capital conservation then buying high quality debt of countries would be a good idea. Singapore or Switzerland are good candidates if you consider it a real possibility that the US could default on its obligations. Otherwise you could hold Treasury bills and roll them over once they mature or you could use an ETF like SHY that holds short-term Treasury bonds.
You could also buy precious metals if you are convinced that civilisation is going to end in the foreseeable future. Drawbacks are fluctuating prices and the complete lack of interest payments.
Generally though there's things like Brokerage Accounts etc which offer higher levels of insurance (SIPC) and easy mechanisms to spread monies across several banks and account services (CDARS for CDs and MMAX for money market accounts).
At that point hopefully you have someone managing your money wisely to help navigate these kinds of things.
'Safe' stocks (utilities, etc), precious metals and real estate are all nominally safe investments as well.