The Searchers
The card that arguably searches Umi.
Warrior of Atlantis
This is the first card in the TCG to include the word "God" in its name
Egyptian God Slime
The most underwhelming card to ever cost $1500
Ten Thousand Dragon
Gorz the Emissary of Darkness
Yugi
Machina Peacekeeper
A Machine-Type monster you control
It's possible to search 3 monsters when you summon this card, but that will probably never happen unless your opponent seriously lacks foresight.
Mekk-Knight Blue Sky
This card featured prominently in the final duel of Zexal, but in real life is just used as a bridge to get to a more powerful monster.
This card was bought out due to rumors about changes to the rules of the game.
Ancient Leaf
Cursed Seal of the Forbidden Spell
Bastion Misawa
Metallizing Parasite - Lunatite
A monster you control
Before Lyrilusc - Bird Call was released, you played this in Tri-Brigade Lyrilusc to increase the probability of getting to Warbler + Sparrow.
Jack-In-The-Hand
This monster was released long before the other members of its archetype. In old formats, control decks and Chain Burn decks sometimes use this card as a board wipe.
Metaion, the Timelord
Alongside a certain Rare from Cybernetic Revolution, this is one of the most prolific FTK enablers in the game.
Life Equalizer
Mirage of Nightmare (in DM)
Apdnarg/Solomon Muto
W-Wing Catapult
V-Tiger Jet
Besides Engage, this is arguably the best archetypal searcher in the game. Unfortunately, it belongs to an archetype that is notorious for being unplayably bad.
In Reaper Format decks that play Metamorphosis, this is one of the best cards to include in the Extra Deck due to its level and multiple powerful effects.
Reaper on the Nightmare
This card, which definitely should not have been printed, was the second card to mention a number over 5000 in its text.
Self-Destruct Button
Raigeki (2 answers accepted)
Joey Wheeler/Marik Ishtar
Second Goblin
Giant Orc
The card that searches Senet Switch specifically
Vaylantz Wars - The Place of Beginning
This monster released alongside a Continuous Spell that would require your opponent to attack only it, creating a soft lock.
Marshmallon
This was the first card to mention a number over 5000 in its text.
Dice Jar
Guardian Angel Joan
Rebecca Hawkins
Burning Beast
Freezing Beast