Wizards of the Coast (WotC) creates Magic: the Gathering. When Chronicles came out as the first reprint set in 1995, this infuriated collectors as it devalued many cards. In response, WotC created the reserved list, and vowed not to reprint paper copies of any cards on the list. This propped up the future of the game as a truly collectible card game.
When the reserved list was originally created, it included all cards from Alpha and Beta, all rares and uncommons from Arabian Nights and Antiquities, and all rares from Legends and The Dark that had not already been reprinted by 1996. As a result, there are some reserved list cards that have always just been unplayably bad. More and more cards were added to the reserved list over time.
The reserve list imposes a block on pure functional reprints only.
Reserved cards will never be printed again in a functionally identical form. A card is considered functionally identical to another card if it has the same card type, subtypes, abilities, mana cost, power, and toughness.
And WotC takes this very literally, so if it's different on any of those factors, WotC does not consider it a reprint. For example, many cards have been reprinted with different colors:
And some reserved list cards have been reprinted with extremely similar functionality:
In other cases, reserved list cards have been reprinted as different types:
Absoutely! The reserved list does not function as a power cap. For example, Roc of Kher Ridges is reserved, but Moonveil Regent was printed long after and is strictly superior other than creature type.
This flows both ways though -- the reserved list is neither a power cap, nor a floor. For example, take one of the best cards of all time:
This extra turns functionality has been reprinted many times -- here are just a few:
The reserved list does not apply to Magic Online (MTGO) or Magic Arena (MTGA) so reprints are available digitally. WotC has repeatedly issued new copies of online-only versions of reserved list cards via Vintage Masters and other Masters Edition sets. Since these sets cannot be redeemed for paper versions of the cards, they have little effect on the collectability of paper editions, and some even believe it brings the paper value up.
Collectors edition and oversized cards are not tournament legal in any format. Any reserved list card can be printed as a special reprint that's not tournament legal, usually denoted by the thicker or larger card stock, a gold border, or a different card back.
At first when the From the Vault: Relics set was printed, WotC did not consider foil reprints to be in violation of the reserved list.
After backlash from the set's release, WotC declared that they would no longer reprint reserve list cards as foils.
Later on though, WotC limited this part of the policy when they started printing extremely limited release promos, mostly Judge Rewards. These promos tend to be so rare that they are priced many times higher than the original print. These are promo reprints of reserved list cards:
There are also a variety of other near-identical reprints that are not considered to violate the reserved list:
Reserved list cards were categorically excluded from Modern when the format was created. As such, Pioneer also has no reserved list cards.
And since no reprints are allowed for these cards, these cards definitionally cannot ever appear in Standard. The reserved list only affects formats that allow cards prior to Modern.
In general, Pauper only allows cards that have been printed at common rarity. It gets inconsistent though when considering promos and digital reprints.
In the beginning of the reserve list, cards were regularly being added and removed as WotC finalized the list. One of those changes was that the list would only include rare cards. This would have meant that no cards on the reserved list were legal for Pauper.
However, once Masters reprints were released on MTGO, some included downshifts in rarities. And since digital reprints do not violate the reserved list, some cards that were originally on the reserved list as rares have been reprinted at common rarity on MTGO. This made select reserved list cards legally playable in Pauper. This loophole is still available -- any reserved list cards printed in digital formats at common would make them legal in Pauper.
Here are the reserved list cards that are legal in Pauper: