In many cricket matches, the decisions taken by the on field umpires get overturned especially in case of LBW dismissals, using the DRS system. What happens if the batsman scored a run off that ball or hit a boundary? Are the runs scored in that ball added to the team's total? Are there any stats about such runs added to team totals?
At least under ICC rules, no runs are scored as the ball is dead. Quoting from the current ICC Test Match Playing Conditions, Appendix 1, Section 3.6(a):
If following a Player Review request, an original decision of ‘Out’ is changed to ‘Not Out’, then the ball is still deemed to have become dead when the original decision was made
Anything else would be very unfair to the bowling side, who will have stopped chasing the ball at the moment the umpire gave the original "out" decision.
If you're interested in a different form of the game, you'll obviously need to read the playing conditions for that format. The ODI playing conditions contain exactly the same wording in Appendix 3, and DRS is not currently used for T20Is.
If I can add to Philip's excellent answer, the ICC makes it clear that the Test Match Playing Conditions "must be read together with the overall Laws of Cricket" (see this link: http://www.icc-cricket.com/news/2015/media-releases/88552/new-playing-conditions-come-into-effect ) and the Law which applies here is Law 23 on the Dead Ball.
(Link to Law 23: https://www.lords.org/mcc/laws-of-cricket/laws/law-23-dead-ball/ )
Law 23.1 (iii) states that the ball is dead when "a batsman is dismissed. The ball will be deemed to be dead from the instant of the incident causing the dismissal". So, even if the dismissal is reversed by DRS, the fact remains that the ball is dead from the moment of the incident causing the initial dismissal. It might also be pertinent to refer to Law 23.5, setting out when the ball ceases to be dead. Once it is considered to be dead, it can only cease to be so "when the bowler starts his run up or, if he has no run up, his bowling action" (for the following delivery).