Depends on the game. Recent Fantasy type RPGs often turn into the discussions about the 5 minute day. Traveller is generally more about how many days have passed as characters track progress on the next skill increase. When jumps take a week, there is a lot of down time for self improvement.
Tracking time during action can be for spell duration, casting time, fatigue, time after calling for an artillery strike before the shells start impacting, attempts to do something to that poor door, or even healing that character that failed at trap removal.
During non action, time tracking often isn't that important. More like is it breakfast, lunch, dinner, time for bed. Unless hobbits are involved, then there are additional meal times.
I have seen the GM do it all and other times where the GM asks one of the players to track the number of time units since X. In one group, I try to note time and place for when the game ended. Another group, the GM does that.
Tracking time during action can be for spell duration, casting time, fatigue, time after calling for an artillery strike before the shells start impacting, attempts to do something to that poor door, or even healing that character that failed at trap removal.
During non action, time tracking often isn't that important. More like is it breakfast, lunch, dinner, time for bed. Unless hobbits are involved, then there are additional meal times.
I have seen the GM do it all and other times where the GM asks one of the players to track the number of time units since X. In one group, I try to note time and place for when the game ended. Another group, the GM does that.

