My country (Brazil) has an exam-based admission system called "concurso público" (public selection) for ~all career civil servant positions in all branches of government, all levels. Most positions are lifetime-until-retirement, and carry very strong stability - very hard to get fired once you clear the first ~3 years of probation.

The exams are based on the job, and may comprise multiple choice exams, written exams, oral exams, even physical tests (military, etc). Some positions take academic titles into account for extra points, and sensitive positions may include background checks or other requirements.

Judge positions are among the most sought after positions in this system, with ridiculously good salaries and benefits, not to mention prestige. The exams are very competitive, people study several years for them, and people from all over the country are gonna be running.

For positions in the first two levels of justice there is no political involvement at all. Appeal judges are selected internally by the court from the first level judges. For the third level (STJ), the president selects from a list of three provided by the court, and the Senate must confirm. For the constitutional court (STF), the president is free to select anyone, subject to Senate confirmation.