When playing card games like President at school, the dealer often declared "Dealer's Respect", which required that no player pick up their cards before the dealer had finished dealing, because the dealer could not do the same.
Is this actually a rule, custom, or convention in any games?
It's a common convention wherever cards are involved; the game doesn't have to be a traditional card game played with a poker or bridge deck.
I think the convention evolved from the trick-taking family, especially Bridge, and the manners and social conventions thereof. Poker, and its emphasis on ensuring a clean deal, is another good possibility for the origins of the convention.
In general, it's just a good idea; here are a couple of reasons why, off the top of my head.
I've commonly heard the superstition that it's bad luck to pick up an incomplete hand. Theoretically that's hogwash, but it actually has some merit; those of us with terrible poker faces give others at the table information not only about the hand, but about each individual card picked up as it's dealt.
However, I can't think of or find any set-in-stone rule (outside of a casino) that requires it to the point of prescribing a penalty for the specific action of picking up or looking at an incomplete hand. It is simply good manners.
Not touching your cards until the dealer has finished dealing is generally considered good etiquette, or "good table manners". I.e. picking your cards up before the dealer has finished is considered rude, rather than cheating.
Etiquette depends on social norms, so it can vary between different countries, different age groups, different social groups, etc. For example, there are probably words you use in front of your friends that you don't say to your parents.
Whether or not you need to follow a particular social rule depends on who you are playing with, the easiest thing is to wait and see what everyone else does.
Yes there is.
The answer differs game by game. Games also differ in the level of codification of the customary procedure. It is a rule with mild sanctions in rubber bridge, a basic necessity in duplicate bridge, a convention in other games, a non-problem in yet others. I will illustrate with two detailed examples.
In Mariáš, the arguably most popular family of card games in my country, there are very specific rules about shuffling, cutting, and dealing. In some modes of the game or after certain circumstances of the previous game, shuffling is prescribed; in others it is prohibited (under a financial penalty), which is very untypical for a card game, and any prohibition on shuffling would be pointless without strict rules on subsequent dealing.
32 cards are dealt among three players as follows: one 5 card block to each player, then 2 cards left as a talon, then again one 5 card block to each player. A bidding conversation ensues between the two players who are not dealers, followed by another such conversation between the higher bidder of the two and the dealer.
It is common (although not mandatory) for players other than the bidder to start looking at and organizing their first five cards already before receiving the other five cards. It is not clear whether the dealer, who enters the auction last, has more or less time than the others to evaluate her hand for possible contracts that way; and it saves time for everyone.
For the opposite example, take bridge. It is played with 52 cards dealt one by one, which takes longer than in the previous example; furthermore, the dealer enters auction first, so no time could be saved by anyone not waiting for the dealer. In its competitive variant (duplicate bridge), the same deal will even serve multiple tables (groups of players) and not all those players will necessarily be present when the cards are being dealt. The laws of duplicate bridge describe the procedure thus: "The cards must be dealt face down, one card at a time, into four hands of thirteen cards each; each hand is then placed face down in one of the four pockets of the board. The recommended procedure is that the cards be dealt in rotation, clockwise. " An even more explicit rule can be found in ACBL laws that apply to rubber bridge as most people know it. ("Players should not look at the face of any card until the deal is completed.")
There are some games (like Roborally) where time matters, so if people pick up cards before the dealer is finished, they're gaining an advantage. At that point it's worth making it an actual rule, not just a convention. But it sounds from your question like you're thinking of games with standard playing cards, and I can't think of an example with those. There can still be an impression of fairness, though - it just feels right when everyone gets to look at their hands at the same time.
