Is it legal for an outfielder to tag out a runner? What about the pitcher?
(Assume for a moment that mischevious martians are playing tricks with the space-time continuum causing said defenders to be close to the runner in the first place.)
Any fielder with the ball can tag a runner out.
Any defender can appy a tag to a runner and he/she will be out.
Forget mischevious martians. It isn’t that unusual for a pitcher to be in a position to field a ball hit to the outfield throw back to the infield from an outfielder. Should the pitcher field such a ball returned from the outfielder, he could tag out a runner if convienent.
The outfielders don’t even have to play in the outfield.
The rule is simply that all fielders, except the catcher, must be standing in fair territory. If you want to play with seven infielders and no outfielders, there’s no rule against it.
I’ve seen an outfielder run a ball in from the outfield after making a catch and tag a runner who had wandered way off the base and couldn’t get back. I also Glenallen Hill get an unassisted DP from RF (I believe) when he caught a fly and then kept faking a throw back to the infield and then just walked the ball in and tagged the guy.
However, if a pitcher is catching a throw from the outfield while standing in the infield, he’s in the wrong place. The pitcher should be backing up a base. The first baseman usually cuts off those throws.
Indeed, except for the pitcher and catcher, the other seven fielders can stand anywhere they like in fair territory. They can all be standing near third base, if they like, or jogging around centerfield, or even inbetween home plate and the pitcher’s mound (although it might be a bit painful).
Zev Steinhardt
A key moment in last year’s playoffs involved a pitcher (Bronson Arroyo) tagging out a runner (Alex Rodriguez). (In this case, the runner was actually called out for interfering with the tag, but a tag would have put him out).
It’s even been done. I can’t recall the teams, but the game was tied in the bottom of the ninth, with a runner on third and one out. A deep fly ball would allow the runner on third to tag and score (winning the game), so the outfielders didn’t even bother playing to catch the deep fly, and moved up to the deep infield , in order to stop any hits through the infield gap.
I can’t remember the outcome, though.
It’s actually quite a standard move. It’s more unusual if a manager *doesn’t * bring in at least one outfeilder in that situation.
It’s also possible for an outfielder to come in and get involved in a long rundown; say there is a man on third and a runner is caught between first and second. The catcher and 3B stay put, and the first and second basemen execute the rundown; but the RF will come in and cover first base in case the runner gets out of the rundown.
If a ball is hit into the outfield and a throw home is expected, the pitcher’s job is to come behind the plate and back up the catcher. It doesn’t happen often, but you’ll occasionally see the pitcher tag the runner at home after catching an off-target throw.
I do recall seeing a center fielder make the final tag at second in a rundown play. No other details, sorry.
It’s customary for the pitcher to move toward first with the idea of backing up the first baseman in covering it. Especially with grounders down the right foul line, the first baseman may be well away from the base in order to catch the ball, and may throw to first with the pitcher covering it and making the putout.
I have seen times when a ball is hit to midfield where the pitcher moves to cover second, with both 2B and SS playing back to catch the ball. I’m not sure how common this situation is, though.
Pitchers may back up first base on balls hit to right field, but often the main backup to first base is the catcher. Most people don’t realize that as exhausting as it is to simply sit back there and call a game, most good catchers run up the first base line on almost every play where the first baseman will be making the putout, as the main backup. Talk about tiring. xo, C.
I’ve gotta ask about this:
If a pitch hits a fielder, what is it ruled as? a ball? (because the pitch never makes it to the strike zone??) Or does some other reg apply?? 
How could pitch hit a fielder other than the catcher? Do you mean that the defense is positioning a fielder to stand in between the pitcher and the catcher?
I don’t think that rule is explicitly covered, but it woud likely be ruled an illegal pitch. If there were runners on, it would be a balk and if there were no runners on, it would be ruled a ball.
And the fielder would be angry, although he probably shouldn’t be standing in that spot.
Zev specifically said that fielders could stand in between the pitcher’s mound and home plate, though it might be painful for them.
And my baseball ignorance is showing a bit… what in god’s green earth is a ‘balk’?? 
We could describe a “balk” in very, very, very long detailed terms, but the upshot of it is that a balk is when a pitcher, with runners on base, makes some movement on the mound that is considered unfairly deceptive to the runner.
Most common is that the pitcher does not come to a full stop before delivering the ball or the pitcher steps toward home before throwing the ball to a base for a pickoff play.
There are a dozen other situations where a balk can be called.
On a balk, all runners on base get to move up a base. If the pitcher makes a pitch on a balk (and time wasn’t called) and the batters hits it, the offense can elect to take the result of the play instead of the one base penalty.
The latter rarely happens.
you might be interested in what Bob Brenley, former major league catcher, former major league manager (World Series winner), and all around knowledgeable guy says about balks - anything that an ump thinks looks unusual might be called a balk. Aside from all the specific acts that can be called one, including inadvertently dropping the ball while looking in for the sign, anything that looks even the slightest bit strange might be called. He says that he’s asked many times for an ump’s clarification, and he’s heard many times that “something didn’t look right” about the pitchers motion. It’s like the Supreme Court’s comment on pornography - I can’t define it, but I know it when I see it.
If you ever hear an announcer or the crowd call for a balk, they will be invariably wrong.
When one is called, everybody just sort of stands around and looks baffled.
The leader in balks so far this year is Brett Meyers of Philadelphia with 4.
Rule 4.03 states:
(Bolding mine)
So, theoretically, a fielder could stand between the pitcher’s mound and home plate when a ball is put into play.
So, what happens if the ball hits him if he’s stupid enough to stand there?
My guess is the pitch would be a ball. See Rule 2.0:
(Bolding mine).
Since the pitch did not enter the strike zone in flight, it would be a ball (as long as the batter doesn’t swing, of course).
As for what a balk is, see Rule 8.05, and award yourself a ticket to umpiring school if you can name all the cases of a balk by heart:
Zev Steinhardt
Zev, it’s interesting that in a) and c) above, the pitcher is directed to either step toward first and throw, or, assuming his free leg is not going to head toward first, to bring it past the rubber and pitch to the batter. But I’ve noticed that many announcers, often former players, and most managers, seem to acknowledge the existence of an imaginary 45 degree line between first and home. And if a pitcher strides to the batter’s side of that line, he’s expected to pitch to the hitter. And lots of guys, with “great pick-off” moves, stride less than the 45 degrees and get away with a throw to first. If I read those rules correctly, a manager ought to be able to easily show where the pitcher’s foot landed - past the “back edge of the pitcher’s rubber” - and contend that the pitcher balked.