How far should commercial jets be from each other when on the runway or while departing?
The FAA's Federal Aviation Regulations (FAR's) are all publicly listed here. 

There are a wide variety of cases to consider on the ground and during departure but you can find a lot of the regulations/guidelines in this document.

For example here is the case for wake turbulance seperation, 


  
  Separate a small aircraft weighing 12,500 lbs. or less taking off from an intersection on the same runway (same or opposite direction
  takeoff) behind a departing small aircraft weighing more than 12,500
  lbs. by ensuring that the aircraft does not start takeoff roll until
  at least 3 minutes after the preceding aircraft has taken off.
  Separate a small aircraft taking off from an intersection on the same runway (same or opposite direction takeoff) behind a departing
  large aircraft (except B757) by ensuring that the aircraft does not
  start takeoff roll until at least 3 minutes after the preceding
  aircraft has taken off.
  


That is just one example, the document is very lengthy and covers a lot of cases, you should be able to find what you are looking for. You should also keep in mind that things like weather and local airport policies will cause the regulations to vary a bit. For example a local noise abatement may cause the seperation/interval timing to be larger than required to adhear to the noise abatement.   

That covers mostly what ATC will see and do, you can take a look at this document for how pilots look at departure procedures.