I have been very happy with the integration with Google Mail and Google Calendar with the iPhone. Gmail has a good IMAP implementation that works well in the iPhone's mail application. Google Mobile Sync's Exchange support works well for synchronizing the iPhone's calendars.
The one problem with the integration with the native applications is that the iPhone's applications doesn't support as many features as Google's. For example, there is no way to send an invite to a meeting to someone else from the iPhone's calendar application.
Google's mobile version of Google Calendar works well on the iPhone. I can use this to schedule a new meeting, and invite other people, all from the iPhone. Also, the new version of the mobile Gmail works well as well. I will not be using these everyday, but when I need a feature that is missing from the iPhone's version of the apps, I will use the web versions.