The Personal version of Office 365 allows users to install Office apps on one PC or Mac, plus one Windows tablet or iPad. The addition of the iPad is new, and enabled by Microsoft's recent launch of Office for iPad.
For users who want/need Office to be installed on more devices, Microsoft is still selling Office 365 Home -- formerly known as Office 365 Home Premium. Office 365 Home allows installation of local Office apps on up to five PCs or Macs, plus five Windows and/or iPad tablets. Office 365 Home costs $99.99 for a year or $9.99 per month.
Microsoft last month removed the requirement that users pay for an Office 365 plan in order to get Office Mobile on their iPhones or Android phones. So anyone, with or without an Office 365 plan, can get Office Mobile for Windows Phone, Android phones and/or iPhone.
Office 365 Personal and Home are designed for home/non-commercial use. Those who plan to use Office for business purposes need additional licenses from Microsoft in order to be in compliance.
Update: For those who don't want or need Office installed locally on their devices, there's always Office Online (formerly known as Office Web Apps). These Webified versions of Word, Excel, PowerPoint and OneNote are free and available to IE, Safari and Chrome users -- and are even available in the Chrome Web Store as of yesterday.