The first successful frameworks were Iron and Nickel.
Iron is designed around a strictly minimal core, with an extension mechanism around the middleware and simpler plugins and modifiers. Nearly everything it does is handled by these extensions, be it logging, body parsing, session handling, and so on. Iron uses no fancy Rust features, which means that it is sturdy, stable, and has no problems running in even an older version of the stable Rust compiler. Iron is at http://ironframework.io.
There are a couple more ...