How many iterations of the legend rule have there been?
There have been three versions of the Legend rule.

From Legends to Champions of Kamigawa (1994&ndash;2004)

We had the rule you described: only one of a given Legend card could be in play. If any newer copies entered, they were immediately removed. Here's what the rule said in 2002:


  420.5e If two or more Legends or legendary permanents with the same name are in play, all except the one that has been a Legend or legendary permanent with that name the longest are put into their owners’ graveyards. This is called “the Legend rule.” In the event of a tie, each Legend or legendary permanent with the same name is put into its owner’s graveyard.
   (If two permanents have the same name but only one is a Legend or is legendary, this rule doesn’t apply.)


During this period there was both a Legend creature type and a Legendary supertype: creatures were Legends (the creature type) and other card types were Legendary (the supertype).

Legends to Ice Age (1994&ndash;1995): Legends initially also Restricted

Initially all Legends were also on the Restricted list, a deckbuilding restriction which meant you could only have one of a given legendary card in your entire deck. WotC did this for flavour reasons and to keep things simple, since you could only play one of them anyway. This change was lifted pretty soon in Ice Age; Mark Rosewater says it created trouble for R&amp;D.

From Champions of Kamigawa until Magic 2014 (2004&ndash;2013)

The second version of the Legend rule was introduced for Kamigawa block in September 2004:


  420.5e If two or more permanents with the same name have the supertype legendary, all are put into their owners' graveyards. This is called the "legend rule." If only one of those permanents is legendary, this rule doesn't apply.


Note that unlike today, we don't reduce down to one copy &mdash; nobody gets a copy of the Legendary card. This change turned Phantasmal Image into an incredibly popular spell for removal: play it as a copy of any Legendary creature, and both head to the graveyard for just {1}{U}. This worked even if the target was indestructible because it wasn't destruction: it was just "put them into the graveyard."

With this change, the "Legend" creature type went away and just got absorbed into the "Legendary" supertype.

Magic 2014 onwards (2013&ndash;today)

The Magic 2014 Core Set Rules Preview article announced the new Legend rule we still have today:


  Let's dive in, shall we? The "legend rule," rule 704.5k for those of you following along at home, is changing. Under the current rules, any time two or more legendary permanents with the same name were on the battlefield, they would all be put into their owners' graveyards as a state-based action. Under the new rules, any time two or more legendary permanents with the same name are controlled by a player, that player chooses one of them and the rest are put into their owners' graveyards as a state-based action.


This segregated the players' boards such that each had their own set of unique Legendaries available to them, and one person playing a Legendary card wouldn't make all the other players' copies disappear.

The actual rules text at current is:


  704.5j If a player controls two or more legendary permanents with the same name, that player chooses one of them, and the rest are put into their owners’ graveyards. This is called the “legend rule.”


Related: Planeswalker Uniqueness Rule (2007&ndash;2017)

Until 2017, there was a separate rule for Planeswalker uniqueness: you couldn't have two or more planeswalkers that shared a Planeswalker type: no two Jace planeswalkers, regardless of their name. (This is the type found in their type line, e.g. Nicol Bolas, God-Pharaoh's planeswalker type is Bolas.) Before 2013, this looked at the whole board (no two players could have a Jace out); the Magic 2014 update (enacted in 2013) also segregated the boards so that two players could have Jace out &mdash; but not two Jaces.

With the release of Ixalan's rules updates in 2017, the Planeswalker Uniqueness Rule went away, and planeswalkers became Legendary instead. You could have one of each Jace, but not two of the same Jace. (Except for Jace, Cunning Castaway due to the nature of his ultimate.)