A few obvious themes and a couple apps associated with them:
– Gaming. Games make up the majority of the most successful paid applications. Examples: Angry Birds, Cut The Rope, Electronic Arts, etc.
– Photos. There are numerous successful apps around photos – either as a network (Path (company), Instagram, etc) or around functionality (Hipstamatic, etc). They are improving a core utility around the device itself. Neither Path nor Instagram launched with web components. And Hipstamatic and others are entirely on the phone.
– Local & Device-Related Companies. Applications where location and/or the device are required components. Examples like FlightTrack, Uber (formerly UberCab), Shazam, etc.
– Messaging & Communication. Kik, Beluga, GroupMe, Tango, etc