What beers are made without malted barley?

Malted barley is the main ingredient in pretty much all beers, even some gluten free beers use extremely low amounts of refined barley malt extract.

If you want a beer specifically not made with any barley at all, I would recommend reading labels and calling breweries. You'll probably have to avoid all mass market breweries, though I believe AB-InBev does make a sorghum lager named Redbridge (no idea if it's totally barley free).