Bicycle carieres for front, rear wheel or seatpost

What types of carriers for bicycles are available ?

The common carrier has a spring clamp and is at the rear wheel fixed.
But mountainbikes usullay haven't an carrier and the standard isn't the best way. 
For this bikes often carriers with seatpost mounting will be used.
For trekking bikers with big lugage the Lowrider is a good solution, this carriers will be mounted at the front wheel.