How can you install subway tile with no grout??

On many projects grout is optional, just attach the tiles close together, not using spacers.

• Do not install tiles without grout in an area prone to moisture or wetness, such as a bathroom or kitchen. Grout joints help keep the substrate dry by sealing it in. Without them, you could be allowing water to seep between the tiles.

Self Spacing Tile is very tight and the grout is more for looks. The shower in the photo is that type on the white tile.

Metal

Reclaimed wood

Wallpaper

Peel & stick for the tile look

Here's a group of images for ideas:

https://www.google.com/search?q=kitchen+backsplash+ideas&rlz=1C1GCEA_enUS814US814&tbm=isch&tbo=u&source=univ&sa=X&ved=2ahUKEwj27Jfyg8rdAhUGLa0KHaOmBycQsAR6BAgGEAE&biw=1280&bih=891#imgrc=_

Sue, I've seen subway tile installed without grout as a back splash on many shows. (Fixer Upper, for one) Don't see why it couldn't be done. Just to be sure follow up with personnel where you purchase the tiles. Good luck.

There is a product available on line and in big box home improvement stores called Grout Renew or Grout Refresh. It is liquid and can be applied just like paint to change the color of your grout and also seal the grout. It is time consuming but well worth the effort.

Butt them together using waterproof Tile Adhesive.

Grout basically is for filling gaps and sealing joints. The grout fills in those gaps and keeps the tile from moving and getting chipped on the edges.