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.
Remember The Milk - Remember The Milk is a task and time management application for mobile devices.
Todoist - Todoist is a to-do list that helps you get organized, at work and in life.
Notepad Checklist - A checklist made by notepad.pw, easy short and fun to use.
Google Tasks - to-do list app that integrates with Gmail and Google Calendar
Harvest - Simple time tracking, fast online invoicing, and powerful reporting software. Simplify employee timesheets and billing. Get started for free.
Things - Things is an easy to use task manager.