Everyone loves the Diabolic Tutor:
But how many tutors is too many? If I'm running a mono-black or black-heavy deck, is there any reason to not just put in four Tutors? What are the possible downsides?
There are two basic reasons to use a tutor:
1) You have a card that you want more than 4 of, but there is no similar substitute available.
2) To be able to have a 'toolbox' of 1-of answers to different types of threats.
So what is the card in your deck that you wish you could have more than 4 of? What are possible substitutes for it in the format you're building for? Is using a turn and extra mana to get at it preferable to the substitute card? The primary reason not to put in a tutor is if your deck can reliably deliver on its designed win condition without needing access to more than 4 of a particular card.
Toolbox decks are usually meta-game haterators, so it's tough to talk about them in the abstract. Mono-black isn't usually known for it though. Toolbox tutors are more often things like Birthing Pod searching up creatures with desirable enters-the-battlefield effects.
Diabolic Tutor specifically, your biggest challenge on that one is how it impacts your mana curve. What are the 5-drop cards in your deck you're tutoring for that you must hit on T5 in order to win? What 4-drop card are you giving up the opportunity to play on curve in order to tutor for something that comes out next turn?
Turn 4 is not a good time to be making a play that doesn't impact the board state. Turn 4 is the kill turn for aggro decks in Standard/Modern that got a half-decent starting hand. Tapping out for a tutor also communicates a lot of information to your opponent. e.g., The only reason you tapped out for 4 in mono-black standard and played a tutor instead of an Obliterator, was to go tutor for an Obliterator. They will do everything they can to be ready for it next turn!
In decks for big multiplayer games, go for it, play all the tutors you can. When games regularly go over 10 turns, getting what you need late is more important than playing on-curve early.
I'd say it's the other way around. When is it worth wasting 4 mana worth of tempo for the gain of exchanging one card in your hand for one from your deck? I think you need a good reason even to run Demonic Tutor.
But as always in MtG it's situational. What do you want to accomplish? How have you planned to win/not lose? We can give the best suggestions if you provide a decklist.
This question is almost too broad. It depends entirely on your deck, doesn't it? If your deck is a fast black aggro that plans to overwhelm with creatures by turn 5 then obviously taking time out to tutor up a card is an unacceptable loss of tempo. If on the other hand you're running a combo where you can't afford not to have drawn all your pieces by turn 5, then some kind of tutoring will be a necessity.
I do think Diabolic Tutor is a well-costed card: 4 mana and a card is a sizeable investment to make, to the point where it may very well not be worth it in any fast environment of finely tuned decks. It's more likely to be worth it in slow formats like Limited (where you plan to win by drawing your bombs) or possibly, as mentioned, Multiplayer - though I would caution that alerting your opponents that you just drew the best card in your deck may increase your chances of them viewing you as a threat!