There isn't a version of Calibre that runs on tablets or mobile devices. There is an app called Calibre Companion which can interface with Calibre on a computer to transfer books via a direct wireless connection or the Calibre content server, but it doesn't contain a reading app.
Some of the more popular non-store reading apps (for DRM free content) for iOS that I can think of would be MapleRead, Marvin, Hyphen & tiReader. All of them do ePub. tiReader is supposed to do a bunch of formats, but I'm unsure how well it handles all of them.
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