North Carolina has nonpartisan judicial elections but most of them really do pit a Democrat against a Republican.
Here are the races:
Supreme Court- Suzanne Reynolds (D) vs. Bob Edmunds (R)
Court of Appeals- Jim Wynn (D) vs. Jewel Ann Farlow (R)
Court of Appeals- Cheri Beasley (D) vs. Doug McCullough (R)
Court of Appeals- Linda Stephens (D) vs. Dan Barrett (R)
Court of Appeals- John Arrowood (D) vs. Bob Hunter (R)
Court of Appeals- Kristin Ruth (D) vs. Sam Ervin IV (D) (High turnout in the Democratic primary lifted both Democrats to the general election in this particular race.)