For simple to-do lists:

• Clear  (iOS & Mac OSX)
• Remember The Milk (all devices)

For capturing notes and organizing research:

• Evernote (all devices)
• Microsoft OneNote (all devices)

Ideal for managing tasks with teams:

• Asana (web & mobile apps)
• Trello (web & mobile apps)

For advanced personal task and project management:

• OmniFocus (iOS & Mac OSX only)
• Things (iOS & Mac OSX only)
• Wunderlist (all devices)