Keep an emergency fund to cover your shelter, food, and other necessities in the event of a layoff or other unexpected event. Common advice is to keep 3-6 months of expenses saved, but that number is highly subjective to your risk tolerance.
The perfect spot for your emergency fund is in a high interest savings account. Usually, these are online savings accounts — a high interest rate is offered because these online businesses require less overhead.
Further Reading
Rates are constantly changing, so it's difficult to recommend a bank. Check out these two resources for the latest interest rates: