For a few years Microsoft has an online version of Sharepoint, but if you asked the partners if they would advice clients to opt for this solution, the answer would be negative. Why? because the Sharepoint online was a very limited sub-set of the Sharepoint on premisses.
Now, with the evolution to the 2013 version, Sharepoint online seems more ambitious, more complete.
Ok, it is still a sub-set of the on-premisses version, but a more complete one. It will be a huge task for Microsoft to have every feature online, but comparing to previous versions, my experience with the current version of Sharepoint online is very positive.
A warning has to be made, Microsoft is still updating their online solution for the 2013 version, this results in mixed 2010 / 2013 versions online at this stage, but it is planned to have a full upgrade to 2013 soon.
How can we know what Sharepoint 2013 versions offer? well, here is a cool and very long article from technet with the indication of the online service description that includes a comparison of the 2013 solution (Office 365, Online standalone ans on-premisses).
To start using Sharepoint online just follow this article from Office 365 and Sharepoint Online Help:
Remember thet developing for Sharepoint online is not the same of on-premisses, so just download this Developer guide:
Is this the time to start implementing more complex Sharepoint solution online? 🙂