Part 1: The phone itself is pretty safe. At least, there have been no cases of anyone remotely breaking into one yet. After 3 years and millions of phones, that's a pretty good track record. Nothing is 100% safe, but I wouldn't worry about this part.
Part 2: The apps are aproved by Apple so there shouldn't be bad apps that steal your data. If that did happen, we'd all hear about it pretty darned fast.
Part 3: Once information leaves your phone, however, you're dealing with the real world. Are you on public wifi? Can you trust it and its owner? Did the website you just logged into encrypt your info before sending it or is it a sloppily coded website? Is that acutally the bank's site you're on or did you click on a phishing e-mail hoax? Did Ebay get hacked today and someone stole data from it? etc, etc...
These are all issues that any device on the internet has to deal with and the iPhone is not any more or less 'safe' than any laptop in regard to these type of security concerns. Only you can say how safe you feel on the internet. All I can tell you is, don't do anything on an iPhone you wouldn't do on a laptop.
