Kill The Past is a blanket label attached to an unspecified number of game developer Goichi Suda's (Suda51) games. Suda's games have many shared elements and his older ones often share continuity too! Due to having a functioning series of games but lacking a series title, the name Kill The Past was selected.
However, as more of his games were released and translated many began to realize that almost every single game of his were connected by varying means and nearly all shared the theme of 'killing the past' so it's often debated what even fits in that label. This is especially odd as it has many arguing which of his games fit into a series and what criteria is needed to select what fits and what doesn't.
Me? Kill The Past just sounds damn cool, doesn't it? I don't really care, all of Suda's games are enhanced by playing more of his games. They're all connected and you should play as many as you can. Don't get too caught up in pedantic quantifications of a man who considers his game the 'punk rock' of video games. If you've listened to punk rock then you know they aren't super keen on following rules.
Kill The Past is every Suda51 game or it does not exist.
Super Fire Pro Wrestling Special
Twilight Syndrome Duology
Moonlight Syndrome
The Silver Case
Flower, Sun, and Rain
Michigan: Report from Hell
Killer7
Killer Is Dead (story)
The 25th Ward: The Silver Case
Samurai Champloo: Sidetracked
Contact
Blood+ One Night Kiss
Death Sentence
No More Heroes
Fatal Frame: Mask of the Lunar Eclipse
No More Heroes 2: Desperate Struggle
Frog Minutes
Shadows of the Damned
SDATCHER
Rebuild Of Evangelion: 3rd Impact
Sine Mora
Diabolical Pitch
Liberation Maiden
Lollipop Chainsaw
Black Knight Sword
Killer Is Dead
Short Peace: Ranko Tsukigime's Longest Day
Tokio of the Moon's Shadow
Kurayami Dance
Bright Red Girl
LET IT DIE
Red, Blue, and Green
Travis Strikes Again: No More Heroes
Fire Pro Wrestling World: Champion Road Beyond
No More Heroes III
Rest In Peace, Chronodia