There's some debate as to whether or not Apple will keep the MobileMe web apps, like Mail, Contacts, and Calendars around after the transition to iCloud. Some have heard no, that Apple will trash them and go 100% apps. Others have heard yes, that Apple will keep them around.
No one outside Apple seems to know for sure. For our part, TiPb has heard there will indeed be web apps in iCloud. At the very least, you'll need a way to access Find my iPhone, Find my iPad, and the forthcoming Find my Mac over the web. Apple has also poured significant resources into the SproutCore-powered Mail, Contacts, and Calendars app -- including a major update to Calendars recently -- and it's hard to imagine them flushing all that effort.
Whether Photo Stream will take over for Photo Galleries, whether Documents in the Cloud will replace the wishy-washy iWork.com, and whether or not the App Store and iTunes store get Web-to-Device push remains unknown.
Even if the native iOS and Mac apps are used far more often, having the web apps as backup is a pretty important feature. We expect Apple to clarify before iOS 5 launches and iCloud comes out of beta this fall.