Today Mann J is hearing Apple Corp v Apple Computers (the court list can be viewed here). The dispute arises out of a pre-internet-age settlement agreement, in which Apple Computers paid Apple Corp, the Beatles' record label, to be able to use the APPLE mark for computers and associated goods, but not for music. At the time (1991), the widespread use of computers for playing music, let alone the iPod, hadn't been envisaged.
The IPKat doubts whether there'd be confusion between the two parties' use of APPLE, particularly since the Beatles' music isn't made available for download, but that's not really the point here. By making a co-existence agreement the parties lifted this matter out of trade mark law and into the realm of contract.