Of course their main market is smart phones and tablets, but this looks especially compelling for servers. Someone like Amazon could buy a bunch of these, attach a bunch of memory to each one, and use a hypervisor to offer something like their newly-announced micro instances. The hardware cost could be lowered, and the low-power nature of the chips would really be useful in large datacenters. Or look at Google: if they can fit the servers for responding to search queries into the 4 GB address space that the Cortex-A15 offers to a single guest OS, this could seriously lower the cost of doing searches -- something that's even more important now that they're doing instant searches as you type.
Of course, it'll be a few years before you can actually buy these. In the meantime, a lot of what I mentioned above can be done with the Cortex-A9, which is just now coming into mass production.
Any IO bound process (that remains IO bound on a slower CPU) is a strong candidate for servers based on the A15. Couple it with simple network coprocessors and you are set.
Of course, it'll be a few years before you can actually buy these. In the meantime, a lot of what I mentioned above can be done with the Cortex-A9, which is just now coming into mass production.