As 'Langware' has replied, if you use the Firefox or Chrome browser, you have the option of installing a small add-on named Webmail Ad blocker.
This not only blocks the ads, but returns the space they would have used - a nice touch!
Unfortunately, if you use IE as a browser you're stuffed... but then that was obviously going to be the case... Microsoft are hardly going to allow you to do that through they're own product (loosing them money).
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You can easily remove ads in Outlook ....
If you use Firefox, try this add-on:
https://addons.mozilla.org/en-US/firefox/addon/webmail-ad-blocker/
If you use Chrome, the same add-on is available here:
http://jasonsavard.com/webmailAdBlocker
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Off topic:
It's surprising they are so seemingly oblivious to the fact they are alienating they're own customers. They are disenchanting them, and turning people further away from IE (no add-ins to deal with such annoyances), and Outlook.com, because of the ads. Way
to NOT listen to your customers, and lower brand loyalty even further!
Windows Phone is about to expire for good ($7.2bn losses), and as for Windows 8, aha, aha,, haaaa. What a curly pile of smelly stuff.
A single interface for everything. What, you don't like tiles on your PC? We don't care... (mmmf mff, ummff - that's the sound of MS stuffing it down your throat). What Enterprise environments - they'll LOVE small tiles and lightweight apps!
No wonder people are shifting away so much, to OSX etc- and that's why they are giving away Windows 10 (not that they'd ever admit that's the reason).
BTW: This is a post from someone who used to be a great proponent of MS, who bought their products, and would sing they're praises. It is no longer deserved.
The are loosing the plot and are in denial. It is SUCH a shame :-(