mlessnau_block_shift is a small but well-formed plugin for selecting blocks of text and shifting the block up or down.
When in Visual mode, pressing
<C-K> will move the selection up, and
<C-j> will move it down. The corresponding functions are
BlockShiftDown, so you can rebind them if needed.
The author, David Wilhelm, notes that the plugin was inspired by a 2012 talk by Douglas Crockford called Monads and Gonads.