Note on some of the comments:
Consistency. Be careful what you wish for

Being consistent isn't the same as being correct. An umpire can be consistently terrible. There are also many who do not understand the rules enough to make such a distinction. Just because a run may score on one type of appeal play does not mean they all do. Obstruction calls and subsequent rulings often have so many variables involved, that a ruling may seem "inconsistent", but isn't. Where you want consistency is the strike zone. At least, your pitcher knows with what they are dealing even though it may be not to their liking.
Invisible. Some folks believe in this myth because somewhere along they way it was a good sound byte. The teams and fans look to the official for their rulings, especially for the close judgment calls, obviously they must be noticed. There have been many umpires and I know a few who take this to heart and will not make that tough call because s/he wants to remain "invisible". They are known as "go along to get along" umpires. They will make calls based on their perception of fair even though it may be in contradiction to the rules. You want to talk about umpires which tell you that they didn't make a call because no one gained an advantage in spite of the rule, that is one of those umpires.
Hustle. This is the best of the bunch. Any game official should always be hustling. Just remember, hustling does not equal running. An official may give up proximity to a play in favor of a good angle. In many cases, an umpire may not get as close to a play as you think s/he should be, but not do to a lack of hustle. It is rare that an umpire has nothing to do other than watch one base and one specific play, so an umpire's position may be determined by their responsibilities on any given play.
All the views voiced in these thread are valid expectations of any sports official and every official should be aware of them. The difference between an umpire meeting your expectation on a specific play or series of plays and failing is the perception on both sides of the issue as to what happened and why, and what should or should not have happened and why.
In the past, the rules of the game were much simpler than today. At all levels and sports, the rules have been adjusted to level a playing field, to make games more competitive, provide more offense/defense (where needed for popularity value), protect certain players at particular positions, yada, yada,yada.
Thick skin/personal. Why is there a perception that umpires should be able to take a load of crap just because the coaches want to give it? What makes people think that screaming and hollering at an official is an acceptable part of the game? How many would accept a game official criticizing a certain play? As a coach, what would you say if an umpire turned to you after ringing up the winning run at 3B on an attempted steal and said, "coach, what the hell are you doing? I've never seen such a stupid call in my life"? Why do you think an official should have to listen to you? Think about the times you have been watching a football or basketball game and the coach is acting like a raving maniac chewing on the referee's ear. How many times have you wondered why the official is just standing there taking it?
Do you know how many times a sports official will toss a coach or player and the response is, "you can't do that, I didn't curse"? When you talk to an umpire, talk about the play. Try to find out what s/he saw, not tell them about the game you think they are missing. A comment made about umpires taking is personal is correct. Some umpires do take questioning a call personally and that isn't right. OTOH, many coaches and players make it personal when their discussion moves away from the play at hand and start talking about the game in general and what they believe are an umpire's shortcomings. I understand they may not believe that is making it personal, but it is. Again, how would you take it if after a costly play and umpire turned to you and said, "damn, coach, you really screwed the pooch on that one"?