So it’s the bottom of the ninth, score tied 1-1, one man on base, batter hits a home run. Being that it’s the bottom of the 9th and any extra runs are superfluous does the game end when the first guy touches home plate with a score of 2-1, or does the game not end until the ‘play’ finishes with the batter touching home and a score of 3-1?
3-1.
It’s different in cricket: if team A has completed two innings, team B is in its second innings, and the scores are tied, then if the batters from team B complete one run, they won’t bother going for the second, even it it would be easy to do. But perhaps that’s because runs are more plentiful in cricket, and the batter scoring the run is not so worried about whether he is x runs not out, or x+1 runs not out.
Nowadays, a game that ends on a home run ends when the batter hitting the homer crosses the plate. However, back in Babe Ruth’s day (I’m not sure when the change was made), the game ended as soon as the winning run crossed the plate, and the batter was credited only with the type of hit that would logically have caused the winning runner to cross the plate. (I’m rather certain that studies have found that the Babe himself did not have any such hits.)
Actually, I believe he had 1 or 2.
Sec. 4.11© of MLB’s official rules states, in relevant part:
–Cliffy
I think that answers one of my questions, which was what happens if the bases are loaded in the bottom of the 9th in a tie game and batter hits a ground rule double. I guess it’s just counted as a single, 1 run and 1 RBI?
Does anyone know what happens in the case of the batter reaching 2nd base before a winning run scores? Is it counted as a single or double?
I think it is counted as a double. I believe the official scorer makes the determination.
Also, at the time, what are now called ground-rule doubles were HR.
(a) Correct;
(b) It is a single.
Official Baseball Rule 10.06(f):
10.06(g) says that a “walk-off” home run is counted as a home run; 6.09 and 7.05 refer to ground rule doubles and other “awards” of bases.
On July 5th, Everth Cabrera of the Padres hit a walk off “single” that bounced over the left field fence with the bases loaded against the Reds. Watch the video (on the right side of the article I’ve linked to) to the end and you’ll hear the great Tony Gwynn, of all people, trying to figure out whether it counted as a 1 run single or a 2 run ground rule double. As others have noted, it was officially scored as a 1 run single, though that feels like the wrong rule. If a home run counts, why not a ground rule double?
At any rate, a single it is.
What if a runner is on first, and another on third, and the batsman hits a single, and the runner on third scores, and the batsman crosses first, but the runner starting from first never touches second and people run in out of the stands?
If the defense bothers to get the ball and appeals to the umpire while touching 2nd or the runner, that runner will be declared out and the batter will be credited with a fielder’s choice rather than a single. If there were already two outs, then the run doesn’t count and the game is not over (assuming it was a tie game to begin with).
What I don’t recall is what happens if there are fewer than two outs and the batter hits an out of the park home run and the runner on first misses second whether the batter gets a home run or not.
No reason why he shouldn’t. Runner on 1st is out and doesn’t score, but the batter gets to score.
(If there were 2 outs, then neither run scores, because the 3rd out of the inning was a force out. No HR.)
Then there’s the Grand Slam Single., when the batter hit a home run but didn’t run past first base. The bases were loaded, but only the runner from third came home; the others touched the next base and started celebrating.
Thanks to all the replies. I wanted to ask about different scenarios too, but not being much of a sports fan I was afraid I’d just embarrass myself!
No offense, but I think I speak for most Americans when I say that we can rarely make heads or tails of that game! 
But that only applies if the frobisher tally thistlewick is in effect.
What if its a 4 or a six - full or partial credit?
IIRC, match-ending fours and sixes are given full credit, unless the batsmen complete the required number of runs to win before the ball reaches the boundary.