Ian Hardenburgh discusses a business planning strategy for enterprises that want to continue to use Infopath forms with SharePoint Online. Office 365 provides a solution.
One of the biggest advantages of using the on-premise version of Microsoft SharePoint includes the ability to deploy InfoPath forms to it. For enterprises that have a lot of information workers that need to readily exchange well-ordered data amongst their collaborators, yet don't want to deal with the hassle of requesting a custom-built form through programmers that they can simply build themselves, SharePoint has become an indispensable BI tool. However, with Microsoft's push toward the cloud, a lot has become clouded (no pun intended) as to whether the same InfoPath features are available in the online version of SharePoint.
InfoPath ships standard with Office 2010 Professional Plus. For the uninformed, it's a fairly intuitive program for designing electronic forms, much in the same vein as ASP.NET web forms, but without all the coding. You're able to attach an almost limitless amount of validation and workflow tasks to most of the same standard set of controls you'll find under an IDE (e.g., Visual Studio) toolbox.
Once a form's design is complete, there are a number of different types of deployment sources one can choose from, such as a shared folder or website, where the read-only form can then be filled out. Although the type of deployment depends mostly upon an organization's business need and available resources, I think it's fair to say that most couple it with SharePoint. This is most likely due to the fact that the forms publish nicely, just as any MS Office document does, in a well-organized folder structure where user-access can be easily assigned. Furthermore, and perhaps more importantly, InfoPath data can also be stored in both internal (to SharePoint) and external sources, such as a SQL Server database, mostly for reasons of reporting or data analysis.
In order to get started deploying InfoPath forms to any version of SharePoint, a user first needs Microsoft Office Professional Plus (InfoPath can be bought separately, but there is little cost-savings in doing so). However, before you go spending hundreds of dollars on the desktop software, consider enrolling in the Office 365 E3 plan (go here), where the office suite already comes standard with the $24 a month per user subscription, amongst other great services -- SharePoint Online being one of them. Once you've got a working version of InfoPath, reference this site to get started working with InfoPath and SharePoint Online.
For enterprises requiring advanced and/or widespread use of InfoPath forms with SharePoint Online, probably the best planning strategy is to use SQL Azure as a SharePoint backend, by way of BCS (Business Connectivity Services). This will allow for a more robust repository of InfoPath form data, where ad hoc SQL Server reporting methods can be applied, similar to your on-premise SharePoint/SQL Server type architecture.