This seems to be a fairly common question, and recently there was an especially well-crafted answer provided on an internal InfoPath user discussion alias. I asked, and received, permission to include it here. (Thanks to the person who wrote this and allowed me to share it with my readers!)
Q: Is there a runtime version of InfoPath?
A: In order to fill out forms created in InfoPath and to take advantage of InfoPath’s rich-client functionality, data validation and offline capabilities, users need a copy of InfoPath installed on their PC.
It is important to note, however, that it is possible to build browser-based solutions based on InfoPath forms. For example, you can build a solution in InfoPath (building a schema and Web services) that can be used for collecting information within the firewall, then use the same schema and Web services for building an ASP.NET solution for collecting information outside the firewall. For business solutions that require a “reach” (browser-based) solution, yet still use the power of InfoPath for the parts of the process that occur within an organization (where InfoPath can easily be deployed), there are two options:
Also, under the terms of the licensing of open and royalty-free XML schemas for Office (including InfoPath), companies can create a browser-based offering (or even a rich client, if desired) compatible with InfoPath. See http://www.microsoft.com/mscorp/ip/format/ for more detail.