Is There Really Such A Thing As Non-stinging Nettles?

Yes, they are most commonly called dead nettles.  And there are actually a few different sorts.

Most nettles that you see are stinging.  They cultivate rough ground.  The sting itself comes from chemicals in the fine hair-like structures that grow on leves (and, to some extent) on stems.  When these hairs break (on even slight contact with your skin), they release the irritating chemicals.

Often growing in the midst of stinging nettles are their benign cousins, the non-stinging sort.  If you see a white flower on a nettle, it is a non-stinger.

All types of wild nettles are important as butterfly habitat and it's valuable to wildlife if you can leave some to grow in your garden, perhaps in fringe locations where they won't seem unsightly or sting you.

There are also ornamental nettles grown for their purple and green pattern leaves.  These lack the stinging hairs and grow broader leves and to a shorter height than the stinging types.