As a trainer, one of the most frequent questions I'm asked is "how many repetitions should I be doing?" The answer to this is solely based on what your training goals are. Different goals call for different repetition schemes. In regards to training the musculoskeletal system, training goals are divided into 4 different categories. In order from fewest to highest repetitions required, those categories are: power, strength, hypertrophy, and muscular endurance. Each category has an ideal range of repetitions required to achieve its specific goal. An important thing to note is that there is not a hard cut-off between each training goal, but instead they overlap into each other. For example, the ideal repetition count for someone training for power is between 1-5 reps. For strength, it is 2-6 reps. This doesn't mean that if you do 6 reps of an exercise, that you are no longer working on power. It simply means that strength is the most prioritized outcome. Even when you get into the muscular endurance repetition ranges (>12), you are still covering a little bit of power, but not nearly as much or effectively as you would be at 1-5 repetitions.
Here is the breakdown for each training goal's ideal repetition range:
POWER: 1-5 REPS
STRENGTH: 2-6 REPS
HYPERTROPHY: 6-12 REPS
MUSCULAR ENDURANCE: 12 OR MORE REPS
Keep in mind that these reps represent the maximum weight lifted for the respective amount of reps. For example, if you are training for power and are doing 3 repetitions of a dead lift, it is assumed that you are completing the exercise with a weight that corresponds with your 3RM (3 rep max). If you are dead-lifting 3 reps at a weight that you can complete 10 reps of, the same principles would not apply to this rep scheme. One thing to note is that the repetition maximum continuum should really only apply to the major muscle group "core" exercises - squat, deadlift, bench press, overhead press, snatch, power clean, clean and jerk, etc. The smaller muscle group exercises, often called "assistance" exercises - such as bicep curls, tricep extensions, leg extensions, etc. - should be limited to loads that don't exceed your 8RM.
Here is a great diagram that shows the rep maximum continuum. It's a great visual of the overlap that occurs between each training goal.
All of the above information is taken from the National Strength And Conditioning Association's Essentials of Strength Training and Conditioning 4th Edition.