In California where I live, I've kept very detailed records of the state, US, interstate, and numbered county routes that I've been on, and even have a KML file showing the roads I've not yet driven, which I can view in my phone.
I've clinched the numbered county routes in 12 of the 40 counties that have such routes: Contra Costa, Imperial, Inyo, Los Angeles, Monterey, Orange, Riverside, San Benito, San Bernardino, San Diego, San Luis Obispo, and Santa Cruz. I agree with Max that Tulare is the one I'm likely to finish last, due to the large number of routes, the fact that most aren't actually signed, and that they're ugly and boring. But I've got all the counties south of there.
As to state maintained highways, I've clinched 34: Alpine, Del Norte, El Dorado, Fresno, Imperial, Inyo, Kern, Kings, Lassen, Los Angeles, Marin, Modoc, Mono, Monterey, Nevada, Orange, Placer, Plumas, Riverside, San Benito, San Bernardino, San Diego, San Francisco, San Luis Obispo, Santa Barbara, Santa Cruz, Shasta, Sierra, Tehama, Tulare, Trinity, Tuolumne, Ventura, and Yuba. The southernmost road I haven't clinched is CA-165 in Los Banos.