Strictly speaking, russet is reddish-brown, but most lists of russet roses also include any beige or tan-colored rose. I've gone through several lists of russet roses and the following pictures are the russets I have in my garden.

Some are difficult to photograph. I'm not a photographer, so I can't give you a technical explanation, but it has something to do with a blue overlay on an orange rose. I guess it takes color adjustments to get the right shade. I've found the color of some to be nearly impossible to capture on film, so there are no photos of Cafe Ole, Cinco de Mayo, Cinnamon Girl, Coffee Bean, Hot Chocolate, and some others here. Maybe someone else has good pictures of them, but my camera refuses to capture them realistically.

This is Amberlight, a 1961 LeGrice floribunda with just enough beige to be included on some lists of russet roses.

This is Ann Henderson, a 2004 Fryer floribunda.

Aschermittwoch (Ash Wednesday) is a 1955 Kordes climbing floribunda.

Black Tea is a 1973 Okamoto hybrid tea.

Ah, now we get to the ones with "brown" in their names. These are the best, in my opinion. This is Brown Study, a 1998 Jerabek floribunda.

This is how Brown Study looks with the sunlight directly on it.

This is how it looks when it starts to fade.

Brown Velvet is a 1983 McGredy floribunda.

This is Brown Velvet with sunlight.

Brownie is a 1959 Boerner floribunda. I think it's my favorite. It goes through several stages and looks great in each. It starts out looking like this:

After it opens, it fades to beige.

Then the outer petals turn pinkish-coral.

Butterscotch is a 1986 Warriner climber. Most of the own-root nurseries list it as JacTan to distinguish it from a 1942 hybrid tea named Butterscotch.

Cafe is a 1956 Kordes floribunda. This is how it looks when the bud is opening.

This is how Cafe looks when it's fully open.

Cinnabar is a 1945 Tantau floribunda.

Cinnamon Twist is a 2006 Zary floribunda.

Coffee Country is a 1997 Viraraghavan floribunda.

Edith Holden (aka The Edwardian Lady) is a 1988 Christopher Warner floribunda.

This is Edith Holden in sunlight, complete with bug.