Google Calendar (Web, Android, iOS) is a Google app that lets you schedule events for yourself, as well as share them with other people. To add an event to both your calendar and a collaborator's calendar, enter their email addresses in the "Add Guests" field:
Doodle (Web, Android, iOS) is a tool that you can use to choose meeting times, schedule events, or collects votes. It's useful for deciding when to meet, signing up to work or volunteer at certain times, or choose from among options - any time you need a lot of people to give input into something.
Pros:
You don't have to have an account to schedule events, and participants don't have to have an account to use your form
Really, really easy to use
Lets participants see what others have put in so everyone is on the same page
Cons:
If there are a lot of choices or options it can get confusing