I'd have to agree with Microsoft here; I've always thought the term "App Store" was like calling your tissues brand "Tissues". They've filed a motion with the US Patent and Trademark Office, aiming to force Apple to give it up.
Intriguingly, they've also used Steve Jobs' words against him. While Apple applied for the trademark in 2008, Jobs apparently was quoted as saying, "Amazon, Verizon and Vodafone have all announced that they are creating their own app stores for Android." You can see where Microsoft is headed with this:
"'App store' is a generic name that Apple should not be permitted to usurp for its exclusive use. Competitors should be free to use 'app store' to identify their own stores and the services offered in conjunction with those stores."
Currently, Microsoft is using "Marketplace" for its Windows Phone 7 app store (sorry Apple, "place where you download apps from"), but even that is pretty similar to Android's app hub, "Market". Really, this argument could go on and on. [PC World]