There are some things that simply can not be recycled. For example, uranium, neptunium, and plutonium wastes, being radioactive, can't be used for much aside from weaponry and for fuel in nuclear power plants. When chain reactions have exhausted the radioactive material, these will have to be disposed of elsewhere. One option is by disposal into a landfill. Another, more likely alternative in the future is the removal of this material from the earth. Although the risks of a failure--such as a catastrophic explosion of the space shuttle as it is going upward--have been trumped up by the media and press, the risks are slight, we still send astronauts to space despite the risks of their dying; accidents usually don't occur all that commonly. When the wastes are safely delivered into space, placing them in orbit will be folly because orbits are (contrary to public opinion) not always stable (hence the International Space Station's scheduled crashing into the earth). Instead, they must be ejected away from the earth. Given a finite propulsion, we can deliver the wastes an infinite distance away from the earth (sounds counterintuitive, but can be proven using calculus and the universal law of gravitation). When the wastes have thus been ejected, the risks will decrease considerably.
As an alternative to sending waste an infinite distance away, it is also possible to send it into the Sun for safe and reliable incineration.