Your iPhone has a built in world clock, but it kind of sucks. Zones is not only a better alternative, it also packs in features Apple's option should have.
As you'd expect, Zones lets you add a bunch of different time zones so you can easily glance at the current time anywhere in the world. Better still, you can change the time in any of those time zones to see what time it'd be elsewhere. For example, you can set Tokyo to 2pm on May 11 to see what time that would be in London, New York and Sydney. There's even a Today Widget so you can access all those times right on your lock screen.
The app is free out of the gate for four time zones, but you can pay an in-app purchase to unlock new themes and an unlimited number of time zones on the screen at once.
Zones (Free/$4.49) [iTunes App Store]