You can sync Base Appointments with iCal, if iCal is connected with your Google Account or Exchange Account.
Note: Currently it isn't possible to sync Base Appointments directly with iCal when it's not connected with Google or Exchange.
iCal sync setup
1. Enable Google task sync in Base (click here for instructions).
2. Open iCal / Calendar.
3. Go to Calendar → Preferences on the top menu bar.
4. Under the Accounts tab in the Preferences, click the + in the bottom left corner.
5. For account type, select Google and enter your Google credentials.
6. After iCal has connected to your Google calendar, click Delegation on the calendar settings and check Base CRM.
Your Base tasks will now be synced with your iCal / Calendar every ~15 minutes.