Amazon's upcoming Android Market competitor, the Amazon Appstore, is in hot water for its namesake. On Monday, Apple filed a lawsuit in a California federal court claiming Amazon had infringed on its trademark of the phrase "App Store." Apple applied for a trademark to this name way back in 2008, but it wasn't approved until January of 2010. Since then, Microsoft has filed a dispute with the trademark office alleging that the grant was improper. That complaint's outcome is still pending.
In the meantime, Amazon may have a difficult time asserting that its use of "Appstore" (as opposed to "App Store") doesn't violate Apple's trademark - it's hard to deny that Apple's App Store is a well-know name in the mobile world.