rust-clipboard is a cross-platform library for getting and setting the contents of the OS-level clipboard.
It has been tested on Windows, Mac OSX, GNU/Linux, and FreeBSD. It is used in Mozilla Servo.

On Linux you need the x11 library, install it with something like:

sudo apt-get install xorg-dev

extern crate clipboard;

use clipboard::ClipboardProvider;
use clipboard::ClipboardContext;

fn example() {
    let mut ctx: ClipboardContext = ClipboardProvider::new().unwrap();
    println!("{:?}", ctx.get_contents());
    ctx.set_contents("some string".to_owned()).unwrap();
}

The ClipboardProvider trait has the following functions:

fn new() -> Result<Self, Box<Error>>;
fn get_contents(&mut self) -> Result<String, Box<Error>>;
fn set_contents(&mut self, String) -> Result<(), Box<Error>>;

ClipboardContext is a type alias for one of {WindowsClipboardContext, OSXClipboardContext, X11ClipboardContext, NopClipboardContext}, all of which implement ClipboardProvider. Which concrete type is chosen for ClipboardContext depends on the OS (via conditional compilation).

rust-clipboard is dual-licensed under MIT and Apache2.