Is there a way (some API) to get the list of installed apps on an iPhone device.
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No, apps are sandboxed and Apple-accepted APIs do not include anything that would let you do that.
You can, however, test whether a certain app is installed:
[[UIApplication sharedApplication] canOpenURL:[NSURL URLWithString:@"thisapp://foo"]
You can get a list of apps and URL schemes from here.