What a coincidence...no sooner did I do a post on Decorati on alternative backsplash inspiration via decorative panels, than I see this post on Design*Sponge! It's a very similar, actually, identical concept, and a good one.
As we see on Design*Sponge famous for great ideas, it can be a DIY project or not. However you tackle it, it's different, it's creative, and it makes an alternative design statement with material other than tile, which is beautiful, of course, often stunning, but, let's face it, there really ARE more possibilities for the backsplash than tile.
Laura is the owner of Open Face Designs and this is a printed design that she created! Laura used plexiglass on top of her printed fabric, but I'd recommend that plexiglass not be used behind a cooktop or range. Glass is a better material, or, I could definitely see engineered stone or corian behind the cooktop to not clash with the beautiful pattern of the fabric.
Think beyond tile...I think in this situation the backsplash looks warm, inviting, and "living room like." Don't you?
Use any kind of fabric behind glass, decorative panels, yarns (wow, that could be amazing!) shade material, take a fuzzy throw blanket, the list goes on. What textures you could dream up! I want someone to put a chenille throw blanket behind glass and then send me a picture when you do, please!