Well I don't die often in Cave Story, but in a Self-imposed challenge (3 HP , polar star, normal missiles, fireball, bubbler, blade) i got a lot of them:
-Got punched by Igor in Egg Corridor (this one is funny)
-Crushed by a SMALL flying Critter in Grasstown
-Monster X proyectiles

-Got caught by Balrog in Boulder Chamber

-Several deaths(like 10 or so) with Core proyectiles
-Fell into harmful water in Last Cave (Hidden) close to the exit

-Three to Ma Pignon falling boulders

-Jumped right into a block summoned by Misery
-DOCTOR TELEFRAG

-Hitting Muscle Doctor with Lv.2 Blade (don't do it pls, is a bad idea)
-Booster right into Sue spining attack in the Undead Core fight

-Falling into a Critter summoned by Draco Misery