I'm not a fan of "cloud" software for the sake of it - much is over-hyped and the main benefit is often to software suppliers. The first program I've used that excels in the cloud is Trello. It is easy to use, free-form and most of all, it helps two or more people coordinate tasks. Most of all, it helps you get things done.
I'm a big fan of to-do lists - but Trello makes it so easy for people to share their to-do lists. There is almost complete freedom in its use - the best way to get familiar with its features is to try it. There's no cost - unless you want to use some of the commercial features.