Batman, created by Bob Kane in 1939, has crossed paths with Swamp Thing several times. Batman is a good judge of character and respects Swamp Thing, as long as he acts justly.
Notable appearances with SWAMP THING:
In the main DC Comics universe, many stories prior to the Crisis on Infinite Earths are no longer considered to be in continuity (i.e.- "they never really happened".)
SWAMP THING (1973 series) #7
While still thinking that the ST is a mindless monster, Batman helps stop the boss of the criminal Conclave responsible for Alec & Linda Holland's deaths. By Len Wein & Berni Wrightson.
BRAVE AND THE BOLD #122 (1975) - Story by Bob Haney and art by Jim Aparo. Batman rescues Swamp Thing who is being displayed in a Gotham City freak show, just in time to combat some experimental bio-spores running amuck. Commander John Zero, previously seen in SWAMP THING #13 (1974 series), appears. He later became the supervillain Saber in the final issues of the original series. Swamp Thing's Gotham adventure is referenced in a newspaper headline seen in Matt's story in SHOWCASE #94-96.
BRAVE AND THE BOLD #176 “The Delta Connection!” (July, 1981)
Swamp Thing helps Batman track down the killers of Catwoman's sister in the swamp. Writer Martin Pasko would later be picked to write the revived SWAMP THING series in 1982.
SWAMP THING #46
In a plot crossover with the Crisis on Infinite Earths, ST briefly bumps into an uncharacteristically confused Batman.
SWAMP THING #53
Batman tries to defend Gotham City against ST's unstoppable assault when Abby is imprisoned. Batman eventually convinces the mayor to release Abby. "If you ever attack my city again, I'll kill you," Batman tells ST.
SWAMP THING #55
Batman attends ST's funeral with Commissioner Gordon and Harvey Bullock, in apology for their mistreatment of ST and Abby.
SWAMP THING #66
To Dr. Huntoon's delight, Batman delivers Killer Croc to Arkham Asylum, but not without sustaining a few injuries. Batman does not meet ST, but Constantine is there.
SWAMP THING ANNUAL #4
A really creepy story in which only ST can cure Batman of an alien disease that is making his body disintegrate.
SWAMP THING 86
In 1800, colonial adventurer Tomahawk battles his nemesis Lord Shilling in the cave beneath the newly purchased property of Darius Wayne. This bat-infested cave will one day become Batman's headquarters.
SWAMP THING ANNUAL #5
When the government apprehends pregnant Abby during Brother Power the Geek's return, Batman appears briefly to ensure her safe treatment. Written by Sandman creator Neil Gaiman.
It's worth mentioning that SWAMP THING writer Alan Moore wrote THE KILLING JOKE, one of the best and most influential Batman stories.