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.
Top Task List - Top Task List is simple, elegant and responsive task organizer.
TimePanic - TimePanic is an award-winning application for tracking time spent at the computer.
Google Tasks - to-do list app that integrates with Gmail and Google Calendar
Toggl - Toggl is an online time tracking tool. It features 1-click time tracking and helps you see where your time goes. Free and paid versions are available.