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.