It took 12 years for Poison Ivy to get an origin story, in World's Finest 251-252. It was actually a Wonder Woman story and not a Batman story.

The Phantom Stranger appeared without an origin in his first issue in 1952, then got four of them at once in Secret Origins #10 in 1987, 35 years later. I'd count that as the biggest, since at least Starman's (simple) origin was implied in his first appearance: he invented the gravity rod and decided to dress up and fight crime as a mystery man. 

The Justice Society didn't get an origin until 1977's DC Special 29 (a wait of 37 years).

The Savage Dragon didn't get an origin until he had been around for about 10 years.  Not a long wait compared to others on this list, but how he ended up naked in a burning field with no memories in his first appearance was rightfully treated as the biggest mystery in his life.  That readers had to wait so long for an answer was impressive.  Pretty cool explanation too.

Actually...

Though readers learned of the Dragon's origin in Image Comics 10th anniversary hardcover celebration, Dragon himself did not until about 10 years after that or so.  Sometimes, the readers will get filled in on details the title characters themselves are oblivious to:

We knew as far back as the first page in Action Comics 1 that Superman was rocketed to Earth as a baby from Krypton.  However, Superman himself didn't learn this until 1948 when he travelled back through time and realised the truth.  So from 1938 to 1948, Superman assumed that he was an Earthman with powers he couldn't explain.  

Details will sometimes get added to a character's backstory to show you either that 'Everything you Thought you Knew was wrong' or 'Now we're Telling you the Whole story'.  

Bat-Man had to wait six issues for an origin (and Joe Chill nine years for a name) but it wasn't until 1955 that we discovered that The Waynes murder was a hit and not random circumstance working against them.  Though I almost never like later additions to a hero's origin, I thought that the Lew Moxon angle in the death of Batman's parents (Moxon was a gangster Thomas Wayne had testified against and who later swore he'd get his revenge on) rectified the fact that had Thomas Wayne not pulled the whole "Take your hands off my wife" stunt, he and his wife might have lived.  I can't help but read Batman's origin (from Detective Comics 33) and notice that Wayne turned an attempted mugging into murder because he chose to fight a gunman unarmed.  The presence of Lew Moxon in his story however, makes it clear that Chill was going to try to shoot him no matter what, so his actions don't come across as reckless and stupid.

The Tick has also never had an origin beyond the fact that he broke out of a mental institution back in The Tick 1 (released 30 years ago).  In fact, aside from a few pieces here and there, we know nothing of what he was doing prior to his first appearance - was he ever a child, where did he get his strength, why is he a superhero, etc. 

Thanks, I got that mixed up. Anyway does the current Joker have an origin? Did he fall into that vat of chemicals?

Far as I know, they haven't altered the chemical plant origin.  Killing Joke was the only thing I saw that really tried to go beyond that, in any fashion, to who he was before the event, without naming him.  It did provide a decent psychological underpinning for that identity.  Of course, it was not meant to be part of continuity and the played fast and loose, after, with what was and wasn't, aside from Barbara's injury being real.

Do we have a thread here for sharing our personal ‘origin’ stories?