Render to texture, use same texture as input in next render call

The effect I want to achieve is a 2D "trail" effect behind the player. Think of it like a conveyor belt of pixels. The player is static while the obstacles are moving towards him.

A similar effect is http://www.youtube.com/watch?feature=player_embedded&v=AfwvklVgef8 where every pixel is moved upwards to get a flame effect. A more correct effect is http://www.youtube.com/watch?feature=player_detailpage&v=Xxi-PG7E5nI#t=10s (look at the corners)

Is there an easy way to achieve this? I know the basics of shaders. I'm using unity pro so I have access to rendertextures.