Grid showing circles to help building round structures, seen from above
/grid 20 /grid circles /grid fixy (before flying up) In circles mode, grid shows which blocks are closest to a circle with a given radius.In this example, grid height is fixed to the ground, not floating with the player.
Example how hexes coords work
With grid hex, the distance numbers are the blocks until the pattern repeats - this is not the "diameter" of the hex!. To create this, you'd need to use /grid 15 9, with the 9 being rounded up from 8.7.
Grid showing a block pattern every 8th block to show where torches should be placed
/grid blocks /grid 8 /grid here When you want to space out torches, or anything else, every X-th block, grid can highlight those blocks.
Torches every 5 blocks light up an area enough to prevent mob spawns
/grid 5 /grid blocks /grid spawns Grid helps you to place torches in a regular 5x5 pattern to light up everything enough so mobs can't spawn.
Grid showing possible mob spawn blocks
/grid spawns This highlights blocks that are dark enough to allow mobs to spawn - red highlights mean mobs can spawn anytime, yellow is for blocks that are dark enough only at night.
Grid showing chunk borders
/grid lines /grid chunks will give you orange lines where chunk borders are.
Building a road
/grid blocks /grid 3 7 Different X and Z coordinates; grid shows where to place lampposts when building a road.
Hex overlay
This is the new (since 1.6) Hex grid overlay. /grid hex, /grid lines.