I've had an iPod touch for a while before I got my iphone, so these are not specifically iPhone apps, but they are the ones I use, how can I only choose 5:
Kindle: Big time, i read a lot on the kindle app. My advice here is to set up a US Amazon profile and use that to buy books, that way you don't pay the extra $2 for the whispersync. Also it means that free books are free and not $2. This app was great in the Touch, but with the iPhone's retina display it is just awesome.
PingChat!: a very similar app to WhatsApp, but free. It has a small add at the bottom of the screen though. The problem with both PingChat! and WhatsApp is that neither of them run on all three of the major smartphone OSs. Ping Doesn't work on BB and WhatsApp doesn't work on Andriod.
Meebo: this is another chat client that works across multiple networks. It does all the major ones, but not Skype. Trillian does Skype, but it is a paid app. At the moment I don't really chat very much on the iPhone, if i start doing that more I will pay for Trillian.
Facebook & Twitter: These are no brainers, I just use the standard apps, but there are many out there, I haven't really gone too far into it. Any suggestions?
TBD: NavApp: I'm still researching this one because they are so expensive, there is little wonder these are the highest grossing apps in the SA iTunes store. I have found no free app that offers Turn by Turn Voice navigation and finds South African locations. There is a thread for this one though. I will be getting one I wish there was a try before you buy option.
I have not had a great experience with PingChat. It is available on BB, but messages just do not go through, app keeps crashing. BB version was not great either (could not send photo's with phone cam, could ONLY browse on device for existing images). IMO, Whatsapp all the way!