FBReader is now available for iPhone/iPad users. This is the official release by FBReader authors, and it is downloadable via the App Store.
Based on the same reading engine, it still misses some features from Android FBReader, e.g. OPDS support. Expected to be added in 1.1 release. On the other hand, the library view and cloud sync are significantly improved in comparison to the Android version.
FBReader for iOS page on the official FBReader site
Features comparison table: FBReader for iOS and for Android
Direct link to the App Store