I learned from another question that Paul uses the same Greek words for fear and trembling (phobos and tromos) in Philippians 2:12 as found in the Septuagint in Psalms 2:11 and 55:5, and it is very likely he was referencing this when he wrote Philippians.
Similarly (though not the same exact Greek phrase), in Mark 5:33, the woman healed of her discharge of blood "came in fear and trembling" (ESV) after Jesus perceived power had gone out from him.
Others have asked what working out one's salvation means; I would like to focus on what exactly it means by these two words, fear and trembling.