Batteries are an option, not a requirement. There are two common setups:
Grid-tied (no battery). The most common and most affordable choice. The grid acts as your backup: you send extra power to it during the day and pull from it at night. The trade-off is that a grid-tied system without a battery typically shuts off during a power outage for safety reasons.
With battery backup. Adds a battery that stores your own solar power so essential circuits keep running during an outage, and lets you use more of your own power at night. This adds cost.
Whether a battery is worth it depends on how often your area loses power and how much you value backup. Many homeowners start grid-tied and add storage later.