Mobile-friendly, minimal, private, and open-source. Works great on your phone as an add-to-homescreen web app, and there is no lock-in with pre-paid hosting.
Reminder Commander - Reminder manager that reminds you about important events in advance.
Todoist - Todoist is a to-do list that helps you get organized, at work and in life.
Date Reminder - Date Reminder reminds you of recurring or nonrecurring events, like birthdays, bills to pay...
Remember The Milk - Remember The Milk is a task and time management application for mobile devices.
Scheduled tasks - GNOME GUI for configuring a users' cron (automatic jobs). Some of its features are:
Google Tasks - to-do list app that integrates with Gmail and Google Calendar