In my hometown of Spokane, WA, most stations use their call letters as their on-air branding, and not their network affiliations. The only exceptions are KAYU ("Fox 28") and KSKN ("The CW 22"). KHQ used to call themselves "Q6," but they've shied away from that branding in the past decade or so.
KHQ and KXLY use their network logos as part of their own logos (NBC and ABC, respectively). KREM had the CBS eye as part of their old logo from the mid-'90s up until about five years ago.
I currently live in the Chico/Redding market, where most stations use their network affiliation as their branding: KHSL is "CBS 12," KNVN is "NBC 24," KCVU is "Fox 20" (formerly "Fox 30"), and KRVU is "MyTV Northern California." The only holdout is ABC-affiliated KRCR ("KRCR NewsChannel 7").