Take offs aren't aborted after V1 which is the calculated based on the stop distance required. V1 is always either equal to or less than VR (the rotate speed). In other words, once you've rotated, you take the problem into the air.
Thats the theory, in practice not always the case though, I was on a Northwest 744 No 1 to land when TWA843 aborted. In practice it's hard for pilots to stick to the mantra although the outcome is predictable re overrunning the runway:
1. Britt Airways Fairchild SA-266TC, Galesburg, IL, 9/24/1986 -- a/c aborted takeoff 5knots above V1. Aircraft stopped on runway.
2. AA. DC-10-30, DFW, Texas, 5/21/1988 --aborted at V1 due to faulty slats disagree light --overran runway due to worn brakes.
3. Britt Airways, Fairchild SA-266TC, Cleveland, OH, 8/16/88--aborted at V1, overran runway.
4. USAir Fokker F28, Charlotte, NC, 4/15/92 --aborted 5 knots after V1, overran runway.
5. Continental Airlines MD-82, Flushing, NY, 3/02/94 --aborted takeoff due to iced over pitot, overran runway -actual speed was 5 knots above V1.
6. SW Airlines 737-200, Nashville, TN, 7/08/96 - bird strike after V1 near Vr, takeoff aborted, overran runway.
7. Air France 747-228F, Paris, France, 9/11/98 -- 3 seconds after V1, aborted takeoff due to cargo bay fire warning, overran runway.
There are a lot of others if you look closely, GA at cough aborted after V2
http://aviation-safety.net/database/record.php?id=19960613-0
Boeing have an interesting paper on RTOs:
http://www.boeing.com/commercial/aeromagazine/aero_11/takeoff_story.html