Homebrewing - Beer, Mead, Wine, Cider

Would I be correct in thinking that unhopped beer is less bitter?

Yes, the bitterness comes almost exclusively from the hops. More specifically, high temperatures cause isomerization of hop oils which contributes to the perception of bitter. The longer you boil, the more bitterness you’ll achieve. Inversely, the less time at high temperatures the hops remain, the less bitter the beer will be. To reduce bitterness (and to increase aroma + juiciness) brewers will add hops near the end of the boil, or even after as the wort is cooling down.

Bitterness from hops is measured in IBUs. A beer with 10 IBU or less is not bitter, 50 is often pale ale / IPA territory and fairly bitter; 100 would be a highly bitter IPA. There are many calculators that will help you estimate IBUs. Note that IBUs are only the scientific measurement of how bitter the beer should be, but the perceived bitterness may be different if the beer is sweet, for example.

You can also add hops at the end of fermentation. This is called dry hopping and will only contribute to aroma and juiciness, and will not introduce any true bitterness. There are modern IPAs out there that are 0 IBU: they only use hops in dry hopping.

Bitterness can also be contributed by roasted malts, where very dark malts, depending on how they’re used can also taste bitter (think bitter chocolate or coffee).

Lokals around here brew a sweet malt beer with no hops. They experiment with smokey flavors for a more whisky kind of taste.

Cider and mead are (usually) unhopped and therefore not bitter. Many beers will list their bitterness as IBU. An IBU below fifteen will be not very bitter.

If you are making a beer, pick a recipe with a low IBU, or use less hops, a hop with lower alpha acid, or with less boil time. Hops does play a role in slowing bacterial growth and balancing the sweetness, so I'd hesitate to take a recipe and just not use hops.