At least 19 states have partisan elections for at least some (though not necessarily all) the judicial offices in the state. Interestingly in the last several years the issue of party designation of certain seats has arisen, West Virginia considering the subject in 2012 and Delaware set to consider its system in 2013.
West Virginia’s HB 4314 of 2012 addressed the issue of Magistrate Court judges (in WV, magistrates are judges of their own court and not as in some states subordinate judicial officers of some other court). Existing law provided that where a Magistrate Court judge vacancy occurred it could be filled until the next election by the Circuit Court for the area. HB 4314 specified that the person selected must be of the same political party as the officeholder vacating the office. HB 4314 was signed into law in April.
Delaware does not have judicial elections, instead the Delaware Constitution specifies a system almost identical to the federal courts: gubernatorial appointment with senate confirmation (albeit for 12 year terms; federal judges serve for life). Governors have opted to use nominating commissions for preliminary screen but are not constitutionally obligated to do so.
Delaware’s constitution does, however, set a mandatory partisan balance in no more than 50%+1 of the judges of the court may be of the same party. Thus, with respect to the Supreme Court the constitution says:
[T]hree of the five Justices of the Supreme Court in office at the same time, shall be of one major political party, and two of said Justices shall be of the other major political party.
There are similar provisions for Superior, Chancery, Family, Common Pleas, and Justice of the Peace Courts and what occurs if there is an even split.
Senate Republicans have announced plans to amend the state’s constitution and require any judicial nominee have held his or her political affiliation for at least two years (h/t to Malia Reddick at IAALS for the pointer). They claim candidates for judicial positions have changed party affiliation to try and become eligible as vacancies have occurred.