Quickly and potentially inaccurate:

Ancient den and artifact lands: Affinity was incredibly dominant in its day. If you're casting spells that have affinity for artifacts, these lands are essentially ancient tombs without the lifeloss. Its been fairly proven that affinity doesn't need them to be a top tier deck.

Birthing pod: a more recent ban, wizards cited it imposing limits on the creatures they could print with it being legal. One of the more controversial bans, but undeniably powerful.
Blazing shoal: in the first modern tournament(s?) infect featuring blazing shoal and progenitus (or gargadon) allowed incredibly fast kills without requiring much mana, allowing the infect player to leave up spell pierce/dispels. Like the artifact lands, infect has proven to be a fine deck without this.

Bloodbraid elf: Was banned at the same time as deathrite shaman due to an overbearing amount of midrange (specifically jund/4 color). Another controversial ban, "died for DRS's sins".
Chrome mox: Either started on the banned list, or was banned in the first wave, wizards tried/tries to ban a lot of the fast mana in an effort to stop the format from breaking turn 4.

Cloudpost: basically tron lands on steroids. Was one of the major players in the first modern tournaments, most of which wizards has banned.

Dark depths: Started on the banned list. Depths + urborg + hexmage is a potential turn two 20/20. Coupled with thespians stage, you have a fairly fast combo thats very difficult to interact with in modern (all of the pieces are lands, and the creature is indesctructible, dodging thoughtseize and terminate.)

Deathrite shaman: Banned due to oppressive midrange strategies. A 1 mana 1/2 that gains life, is a wincon, produces mana, and is gravehate in green OR black is simply too powerful.
Dig through time/treasure cruise: banned at the same time, u/r delver was the primary deck using these cards, but jeskai ascendancy was popular too, and even burn splashed for cruise, and most blue counterspell decks played dig, namely scapeshift, jeskai, and ad nauseum. Being able to turn a underused resource (graveyard) into massive card advantage is strong, and playing a deck that doesn't play either of these means starting with a big disadvantage.

Dread return: always banned in modern. If you think dredge is bad now, it could only be better. Being able to reanimate an elesh norn, iona, or flamekin zealot for no mana, and recoup the sacrificed creatures with bridge from below is part of what makes legacy and vintage dredge so powerful.

Eye of ugin: banned following eldrazi winter. The colorless eldrazi decks could often kill in the first couple of turns, after dumping out a pile of eldrazi mimics for free, and simply playing fairly strong creatures for much less than their intended mana costs. Eldrazi was, and still is, the only deck that plays sol lands in modern, barring the possible exception of darksteel citadel. (Though thoughtcast is the only played card that takes advantage of this).

Glimpse of nature: has always been banned in modern. Legacy elves is capable of consistently killing on turn 3, with a rare turn 2 kill, primarily because of the insane card advantage glimpse can provide. Without cradle, such fast kills are unlikely, but being able to commit half your deck to the battlefield while holding the other half in your hand for 1 mana is pretty good.

Green sun's zenith: banned for diversity reasons. Being able to turn 1 tutor a dryad arbor for ramp, and later being able to tutor a knight of the reliquary, or even a primeval titan means that gsz is both incredibly strong early and late, and has no real downside to including it. Nearly every green deck would include it.

Hypergenesis: similar to living end, cascading into hypergenesis is a potentially fast combo, even without much fast mana. Living end however requires you to play lots of subpar cyclers to make the combo work, where as hypergenesis just lets you play emrakul.

Jace / stoneforge mystic: banned due to standard dominance, theres no real argument that a huge number of white decks would play stoneforge, and a huge number of control decks would play jace. Somewhat controversial as well, due to them never having seen the light of day in modern.

Mental misstep: banned due to diversity. Mentap misstep has targets against nearly every deck, but the real issue is that the best way to beat a misstep is your own misstep. While people saw street wraith and probe and claimed that every deck would 56 cards + probe, with mental misstep this more or less actually happened.

Ponder / preordain / rite of flame / seething song: Banned due to storm. While originally storm was a genuinely strong deck, seething song seems to have been banned more due to wizards' fear, or simple dislike of solely spell-based combo in modern. Ponder and preordain are fairly controversial bans individually.

Punishing fire: combos with grove the burnwillows to allow one to machine gun down all small creatures. Small aggro strategies (infect, bushwhacker zoo, elves, etc) would have a pretty tough time dealing with this.
Second sunrise: The original modern eggs deck was fairly powerful, but nearly always took forever to safely win, resulting in potentially half-hour turns. While this isn't the most fun for an opponent to sit through, this played havoc with tournament schedules. When tournament matches go to time, the game gets 5 more turns before it ends. However, if one of these turns is a half hour long, you only need one eggs player per round to add hours upon hours of delay over a whole tournament.

Sensei's divining top: While it would enable the legacy counter-top deck to exist in some regard, wizards has cited time as the primary reason top isn't legal, similar to second sunrise.

Skullclamp: an infamously powerful card, being able to turn tokens, mana dorks, or other small bodies into cards for a small amount of mana gets powerful pretty fast.

Splinter twin: while the deck was powerful, and wizards cited power/diversity reasons as the main concerns, shaking up the modern pro tours is often mentioned. Easily the most controversial ban.

Summer bloom: amulet bloom was able to fairly consistently break the turn 4 rule, and was difficult to interact with, especially with the spell based hivemind combo, and the land based engine.

Umezawa's jitte: banned due to standard dominance. It would likely become an auto include in some number for any aggressive deck. Being able to kill creatures, gain life, or deal more damage is fairly powerful, but jitte does them all in nearly the best ways possible.

This got long, and its probably not totally accurate, but hopefully its atleast marginally informative. Anyone who has anything to add would be appreciated.