Microsoft has released Outlook.com, what they consider to be the next-generation of email. And much to their credit, Microsoft have gone above and beyond to make sure you can access it not only on the web, but from any and all of your devices, including the iPhone, iPod touch, and iPad.
Better than the website, you can set up the built-in iPhone, iPod touch, or iPad Mail app to get your Outlook.com email.
And you're done! You will miss out on any web-specific features, which are what Microsoft is working to make all shiny and revolutionary, but you will get all your mail in the unified inbox, right beside iCloud and Gmail if you use those services as well.
Note: You can also set up Outlook.com as Exchange ActiveSync. Just follow the same steps above but choose the Exchange button and use m.hotmail.com as your server.
You can login to Outlook.com on your iPhone or iPad, the same as you can login to it on your Windows or Mac PC.
If you're on your iPhone, you'll get a warning saying you need to upgrade your browser to a newer version of Safari. Ignore than and tap on Continue. That's just poor interception (since you can't update iPhone Safari the way they imply.)