I actually use Event Calendar, which has been abandoned for some time. Looking at the alternatives listed in the Plugin Directory, Calendar, Events Calendar, and Gigs Calendar add full calendar management features to WordPress. While ICS Calendar, iCal Events, and Upcoming Events, simply offer the ability to display calendar data from elsewhere.
What I liked about the old Event Calendar plugin is how events were posts. Creating an event started with creating a new post. Searching and browsing events was the same as for posts. I haven’t yet tried any of the alternatives, but if none of them treat events as posts, I may find myself re-working the old plugin for better compatibility with current WordPress.