Detective Comics #585 - The Ratcatcher & Detective Comics #586 - Rat Trap (1988) - The First Appearance of Otis Flannegan/the Ratcatcher. This is also the definitive Ratcatcher story.
Detective Comics #679 - Prodigal Three : The Vermin Factor (1994) - A short but sweet Ratcatcher story.
Catwoman #26 - Rats (1995) - This has Catwoman, Catman & Batman all against the Ratcatcher and has Ratcatcher trying to pull off the biggest scheme of his life.
Batman #555 - Trapped Like Rats (1998) - This issue has a nice little Ratcatcher appearance.
Robin #68 - War Beneath the Streets! Part One: Rats! (1999) - This issue teams the Ratcatcher up with Mr. Freeze during the huge No Man's Land arc.
Infinite Crisis #1 - Infinite Crisis 1 (2005) - This issue features the last appearance of the pre-New 52 version of the Ratcatcher.
Batwing #27 - Not All That Glitter & Batwing #28 (2014) - These issues feature the first appearances of the Ratcatcher in the New 52 continuity. It also gives him a new costume.
Batwing #30 - Underbelly to Batwing #32 - Family is Everything (2014) - These Issues have the Ratcatcher as a major villain for Batwing to face.