There's no reason why you shouldn't be able to omit texturing on modern hardware if you really wanted to. Given that we're dealing with programmable shading as a matter of course these days, you could just as easily write a fragment program that does no texture reads at all. Though texturing is natively available always (i.e. you don't have to turn it on per se), you don't actually have to use it.
As for, if anything has released in recent years without texturing... outside of games that do some 3d on mobile devices, I don't think you'll find it. And even then, I'm not sure, as 3d gfx on mobile games didn't really pick up until the hardware advanced to the point of being very feature-rich (DX10 level).