What is the difference between on time and in time?
‘In time’ means to be at the edge of the specified time, with no spare time left.
‘On time’ means to be punctual, with spare time left.
To clarify that here are two examples:
I arrived just in time to catch the train. (So any later and you would have missed it).
I arrived at the station on time (So you had time to spare and spent some time actually waiting for the train).
In time is frequently used with the word ‘just’ as in our example above. See the British Corpus for more examples: http://www.natcorp.ox.ac.uk/
robertdesenior 
I think this explanation is actually incorrect – “in time” can be used to mean with no spare time left, as in “just in time”, but it more generally means “by the time required to be able to do something”. See the following examples:
・We arrived at the station in time to eat lunch before catching our train. → (We had the requisite amount of time, with no implication of “cutting it close”. In fact, we had extra time that we used to eat lunch [secondary event] before catching our train [main event].)
・We arrived at the station in time to catch our train. → (We arrived at the station by the requisite time to be able to board the train – this could be seconds or minutes ahead of departure; no distinction is made here about the buffer of time remaining, just that the planned activity was still possible based on the time.)
・We arrived at the station just in time to catch our train. → (We arrived at the absolute outer limit of the required time to be able to board the train; any later and we would have missed it. The qualifying adverb “just” is necessary to make this distinction.)
On the other hand, “on time” simply refers to being in agreement with a predetermined schedule. See the examples:
・She arrived on time for her appointment. → (If she planned arrive at noon and arrives at 11:45, she will be present at the intended time and is therefore on time. If the plan was to arrive at noon and she gets there at 11:59, this is also “on time”, as it is still in accordance with her plans.)
・Get me to the church on time! → (Get me to the church at or by the planned time! “With time to spare” here is the conventional implication, but not contained within the wording itself.)
・The project must be completed on time. → (The project must be completed on or before the planned date/time. If the deadline is 8/30, this can just as easily mean 8/15 as 8/29, or even on the final day itself, 8/30.)
If one wishes to specifically indicate an excess of time before the absolute required point in time, “ahead of time” or “with time to spare” can be used.
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