I agree with those who say that surfaces that are either difficult or expensive to change, should be as classic and timeless as possible. That's why I would not want a highly memorable, super-bright, or super-patterned, backsplash. If you got tired of it, it's a major pain to alter.
So, for me, a backsplash with plain tile and no patterns would be my choice. Within that confine, there still are options. Oh, and apart from tile, I Iove painted beadboard as a backsplash, below. It's so neat the way it continues up through the glass-fronted cupboards here:

While subway tile is a hundred-plus years old classic, it's been so popular in recent years that I'd prefer a little variation on that. Maybe like square tiles with a little sheen, stacked one on top of each other? I love this kitchen below, what we can see of it!
In fact, I do prefer a "stacked" look in any tile, rather than the overlapping style. This kitchen below is rather modern, and the stacked, vertical tile looks good with that, I think. Wouldn't want that much open shelving, but this too is a handsome kitchen.
The "slab" backsplashes became very popular. Stone veining can be beautiful, for sure, as long as it isn't too wild and crazy. I did see one that was patterned boldly, like a zebra. I'm guessing these marble slabs require specialized skills to install properly.

I can't even imagine having the means to have an old, mortared stone backsplash or wall like this one below, but what a dream! Even if it crumbled a tad, it would be worth it-- so warm and appealing. (But a nightmare to clean?) Let's not be practical...

Not everyone agrees with a preference for more low-key hard surfaces, of course. What sort of backsplash do you gravitate toward?