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.
Date Reminder - Date Reminder reminds you of recurring or nonrecurring events, like birthdays, bills to pay...
Todoist - Todoist is a to-do list that helps you get organized, at work and in life.
GoGetter - GoGetter is a task management system based on David Allen’s ever so popular Getting Things Done...
Remember The Milk - Remember The Milk is a task and time management application for mobile devices.
Trello - Infinitely flexible. Incredibly easy to use. Great mobile apps. It's free. Trello keeps track of everything, from the big picture to the minute details.
Google Tasks - to-do list app that integrates with Gmail and Google Calendar