Short Answer:
Did Batman and Wonder Woman share a more than platonic relationship? And was it canon?
- Yes and yes. A brief relationship is hinted at in the DC Animated Series, Justice League Unlimited (You can see an episode featuring that relationship called "This Little Piggy.")
They also considered a relationship in a previous continuity, Post-Crisis in the Justice League of America comic written by Joe Kelly in The Obsidian Age Saga.
With the creation of the DCnU, any previous relationship between the Batman and Wonder Woman has been erased. Now Wonder Woman and Superman are an item but no knows how long their relationship may last.
DC Animated Universe
The DC Animated Series played with the idea of Batman and Wonder Woman as potential significant others:
A chief writer on this storyline is Dwayne McDuffie - creator of Static Shock and one of the larger story arches for the DCAU. Notable episodes where Wonder Woman and Batman hint at something happening are, "Maid of Honor," "Starcrossed," "This Little Piggy," "A Once and Future Thing, Part 1," and "Kid's Stuff."
In the first of these, Diana and Bruce have a lengthy dance and flirt before getting around to saving the day. In the end, Diana guesses that Batman is Bruce Wayne, but he plays it off. In "Starcrossed," the Justice League shares their identities before separating to rendezvous at a later point & Diana & Batman go their own way. To avoid capture, they "pretend" make out.
This clip from "This Little Piggy" pretty much sums up why they don't really ever work out.
In the DC Universe
As to whether Batman has ever had an interest in Wonder Woman, it has been shown in several continuities that Batman and Wonder Woman have had more than passing interests:
- They are both martial artists, conversant in several styles. They have been seen to train against each other improving their abilities.
- Wonder Woman gets to train with an excellent, highly trained fighter, and Batman gets to fight against someone who has superhuman speed, strength and reflexes. Both are improved by the experience.
- They both study history, language and are very well traveled.
- Both are highly intelligent and scholars in their own right, Bruce is self-taught, Diana trained by the scholars of Paradise Island.
- Both are highly attractive, it only makes sense they might gravitate toward each other.
The Justice League comic series has hinted on and off depending on the writers but only Joe Kelly has ever done anything serious with it.
Joe Kelly decided to explore such a relationship during his 2003-2004 run on JLA. During the storyline "The Obsidian Age," in which the Justice League journeyed into the ancient past in order to save a time-lost Aquaman, Batman and Wonder Woman prepared to fight their enemies to the death and, before doing so, they surprised one another (and a lot of readers) by sharing a kiss. Once all the resurrection, time-travel, villain-fighting and day-saving was out the way, the two put off having to talk about their kiss for awhile, with Batman being the more reluctant of the two, even standing Wonder Woman up on at least one occasion.
Ultimately, Wonder Woman used Martian Manhunter's Martian Transconsciousness Articulator, a doohickey that plays out various possible futures in dream-like fashion for the user, in order to determine that maybe she and Batman were better off just being friends and teammates. REF: Comic Alliance > The Many Loves of Wonder Woman
Batman and Wonder Woman share a kiss before dying in The Obsidian Age saga
Corrections and Clarifications
This question is rife with inconsistencies, so let's clear them up.
- Wonder Woman and Super-Woman are two different characters, though their physical powers are almost the same.
- Wonder Woman first appeared in All Star Comics #8 (1941)
- Super-Woman first appeared in Justice League Vol 1, #29 (1964)
- Wonder Woman has been around since the Golden Age of Comics and has had her own comic for over forty years.
- Super-Woman is an alternate Earth (Earth-3 by Pre-Crisis parlance) character who shared an origin with Wonder Woman, having come from an island of Amazons. But Superwoman was not an emissary of Paradise Isle, she was a renegade who left the island for her own reasons.
- Super-Woman would later join the Crime Syndicate from Earth-3 consisting of Ultraman, Owlman, Power-Ring and Johnny Quick. This would almost be the same Crime Syndicate of Amerika to appear in the Animated film: "Justice League, Crisis on Two Earths."
(Well, not exactly. The parallel Earth this group originated from was destroyed. They were later reconstituted on an Anti-Matter Earth after the Crisis. Now with the reconstruction of the DCnU, there is an Earth 3 again, so no one has decided what to do with the Anti-matter CSA. If you want to know more, check out Cosmic Teams, Crime Syndicate of Amerika entry. It's awesome.)
Crime Syndicate of Amerika (the Anti-Matter Universe version)