That is possible using InfoPath and SharePoint though it would really depend on how flexible you need the forms to be. InfoPath also stresses functionality over aesthetics so the final forms might night have the exact look you are looking for. Infopath also requires that the users of the form also have InforPath installed in order to get the full functionality. There is a web-based option for it but it does have slightly reduced capabilities.
If you are targeting SharePoint 2013, then the door is really wide open as literally anything can be used to create custom forms via the new AppWeb model. This is still a very new area but the possibilities there are limitless.
Lastly, you could go the home-grown route and merely use the PageViewer web part in SharePoint to tie into your own custom Asp.Net solution that could use SharePoint Web Services for data storage. This model is very close to what is done in SP 2013 anyway, though SP 2013 does have cleaner integration.