Large format tile as a backsplash does work, and I use it often. I would limit the ornamentation as that can get busy looking. Most of us have at least some items on the counter, and that along with an "ornament" may be distracting. If you plan on doing it yourself, the larger tile is more challenging to install, as the wall has to be built very straight (not always the case). Many will try to discourage you, but a good installer can do it. Never put tile behind the cabinets - from counter to bottom of cabinet normally measures 18" as 0825sam says. The cabinets are attached to the wall, and must be flush with the wall. Tile behind would interfere.

Creates a really clean look to have large tile with few grout lines from counter up.

Do a search for 'self cleaning tile'. Really! I used it with a client as a backsplash a few years ago. She is a fanatical cleaner! We did a leather finish black granite counter top, and black textured 8 X 14 +/- self cleaning tiles horizontally on the backsplash, with the 4 X 4 accents. The porcelain tile glazing "sheets" the water off instead of repelling it, and thus takes the 'dirt' with it, instead of spotting. The tile we selected was available in about 4 colors at the time.