You may find this article is useful for reference.  I happen to be a Google fan, and my internet experience is defined by Google:

• gmail
• Google Calendar
• Google Reader
• Google Maps
• Google Personalised home page
• Browser, phone or blackberry

I might add this is by choice, having tried them all, and going back to make sure once in a while too.  I can get Google things on any device, easily quickly, personalised, and customised to work well in each device.

My point is that whether you are a Google fan or not, they do a good job at defining the cross channel experience, and how to handle the quirks of each channel. 

This article provides insight to Google strategy from Deep Nishar, director of product management for Google.

The company has steadily introduced new services designed specifically for the small screen. In January, it released Google Personalized Home, which lets people access Gmail, news, RSS feeds and other information from their personalised Google home page on mobile phones and PDAs. The service is free in the US and works with any phone that contains an XHTML-capable web browser.

This summer it launched a downloadable Java application for Google Maps, enabling mobile phone users to get information about local restaurants and cinemas, as well as live traffic information on the map.

And this month, it improved its mobile Gmail client to allow quicker access to the application. At the same time, Google has been busy developing partnerships with mobile operators, such as Sprint Nextel and Cingular Wireless. It’s also been testing new business models, such as text-based mobile advertising, and more localised advertising.

With nearly three billion mobile-phone subscribers in the world expected by the end of 2007, Google sees great potential for extending its presence throughout the world using the mobile platform, said Deep Nishar, director of product management for Google.

Source: Google takes aim at a mobile future – ZDNet UK