sooo pretty!

*stands there blushing and bowing her head with a smile. She clasps her paws in front her her tummy and turns back and fourth where she stands* *^!^* Thank you very much! *^!^*

*giggles and pounces* meww!

*^!^*

Wow, now there's some fanfic demanding to be written. Starfleet from a furry universe visit the 60s Batman era.

If so, I imagine that Gary Seven, and his secretary, from the last episode of Season 2 of Star Trek: "Assignment: Earth," in which the Enterprise goes back in time to 1968:
http://www.imdb.com/title/tt0708419.....ref_=ttep_ep26

I can also picture Batman and Robin using the batropes to climb up the side of a building, and being greeted by a Starfleet crew-member who just happens to stick their head out the window of that building; not unlike the variety of celebrity guests that did the same thing, during the end of Season 1 and throughout the Season 2 of Batman; including an out of uniform Colonel Clink! ^!^

I have a feeling that Adam West's "Lawful Good" Batman would not get along too well with William Shatner's "Chaotic Good" Captain Kirk. What would be worst if if the two of them start arguing in the stop-and-go manor that they both tend to speak in. >!<

Well, Batman's lawful good meant he would follow someone in legitimate authority. Kirk also has the ability to sway people to his point of view.
Maybe...maybe Batman met Kirk at the start of his career. Maybe the Bat-computer and "way too advanced for the 60s" gadgets and tech are gifts from the Federation.

Hmmmmmmm . . . I can imagine it taking place on an alternative Earth. I can imagine the crew of the Enterprise taking part in this Batman's origin story, years before the television show takes place. Perhaps the crew of the Enterprise encounters a Earth filled with super criminals, but no super heros. It then becomes their job to search their computer's memory banks for a comic book hero that best is the best fit for Billionare Bruce Wayne. I figure Kirk would meet Wayne after being abducted by a super criminal. Perhaps Wayne and/or Grayson are abducted as well.

There are some elements of whackyness within the fabulous Bat Cave that desire explanations. For instance, the reason that everything is clearly labeled, is because,at first, Wayne and Grayson don't know their way around the Bat Cave well-enough to do without them (and achieve any level of efficiency). Later, they remain as a reminder that there is always something new to be learned. All other elements of whackyness might have come from an encounter with Mr. Mxyzptlk of the Fifth Dimension (But I guess that allows Superman to exist, as well), or pehaps the fabulous Bat Cave is scrambled or destroyed by a super criminal; leaving Batman and Robin using their limited knowledge and resources to restore the fabulous Bat Cave. Eliments of a food replicator being wired within the Bat Computer might explain why the thing is capable of giving it's answer in the form of pasta. The whackyness is never questioned because all that matters to them is that it works.

You totally need to write this fanfic.
Suggestions: Bat-Mite is Batman's wacky imp nemesis (there's a great comic called World's Funnest showing him and Myx fighting)
Maybe the reason Wayne and Grayson are still learning how to use the items in the BatCave is because they didn't invent them...

You may want to be the one to write this story. At least you have a much greater knowledge of the stories within the comics. I am familiar with "World's Finest," but I have never heard of "World's Funnest." It sounds quite lighthearted and is probably just for laughs.

Yes. It was a single issue where Myx and Bat-Mite fight each other in various versions of the DCU like the Silver Age, the Dark Knight Returns, drawn in the appropriate styles. Good tongue-in-cheek look at them. Worth reading.

It does sound like a worthwhile read indeed! ^!^

If we're ever going to be at a meet a the same time again, remind me to bring it. It's a quick read.

I figured out how to get the Enterprise to Batman's Earth! You see, Dr. Smith gains possession of an alien device that bridges the gap between the Irwin Allen universe and the Gene Roddenberry universe. (The irony being that, not only has the the crew of the Enterprise come across lost colonists before, but they have also come across at least one planet that was an exact match for Earth, except for it's alternate history. Hence, within the confines of this story, it is possible for all three "universes" to coexist in the same "universe.").
When Smith uses the device to send out an SOS, it is the Enterprise that receives and answers it.
At this point, I could limit the number of additional characters to just Dr. Smith, rather than having to write for the entire eight-member cast of "Lost in Space." I could even have just Dr. Smith, Will Robinson, and Robot travel aboard the Enterprise. However, I shall attempt to see what happens when the entire ensemble gets involved.
I foresee such a story as being almost entirely character-driven, relying only on certain "anchor points" to ensure the story has a plot (and a point! After all, this is supposed to be about how Batman got his "wonderful toys" :p ).
I think you can tell that it is Smith who shall send the Enterprise to Batman's Earth, and that he shall interact with at least one of Gotham's favorite criminals. He may even help one or more of them become super criminals, while our heroes help Bruce Wayne become a super crime-fighter. In either case, I expect that Spock shall explain that, on this Earth, every major city has at least one super hero, except for Gotham.
In the end, Captain Kirk reluctantly returns the Robinson Family to the crashed Jupiter II. He explains the Prime Directive and the importance of upholding it. While everyone else agrees, Dr. Smith whines, complains that it's unfair, and points out how the Prime Directive was violated back on Batman's Earth.
Kirk stares Smith down: "I intervened by giving aid to law enforcement in order to restore balance after someone else's intervened by giving aid to criminals! And if you can't understand that, then understand this: That same law is why I'm not leaving you marooned on the same mining colony where I left Harry Mudd! Not to mention the fact that, for some reason, the Robinson family wants to have you around."
"Yes, yes, the Robinsons are a fine family, every last one of them . . ."
"Kirk to Enterprise, four to beam up."
" . . . And, of course, the Prime Directive must be obeyed. It wouldn't be right going around tampering with other people's timelines, would it? . . . Wait! Who's Harry Mudd??! Who's Harry Mudd?!!! Come back here!!!!!! Who's Harry Mudd??!!!!!!!!"
Dr. Smith repeatedly points to his chest as he snivels: "Oh the pain! The pain!" He sits on a rock and continues to whimper and mutter to himself. Will Robinson approaches him (from behind) and places his right hand on Smith's left shoulder, and says, "Don't worry, Dr. Smith, I know we'll get back to Earth, our Earth, somehow."
Dr. Smith responds, "But how?! And when?! And what am I to do in the meantime?! I don't think I can bear another day of being marooned here on this planet!"
"It's not that bad, Dr. Smith. Engineer Scott did repair our water reclaimer, and Dr. McCoy left us an assortment of medical supplies. Captain Kirk even gave us enough food to last util we start harvesting our own again! Mom's cooking some of it right now!" Will takes a hold of Smith's left hand, tugs on it, and says, "Come on Dr. Smith! Mom's cooking will cheer you up!"
Dr. Smith whines, "I'd rather starve than face everyone! Although, it would be rude to not accept a dinner invitation." He slowly gets up and allows Will to lead him, "And it would be an insult to the chef if I didn't take a bite or two. Come my boy! We musn't leave the others waiting! Let's get moving beforemy diner gets cold!"
"That's the spirit Dr. Smith!"
"You know my dear William," Dr. Smith says in confidence with Will, " there is something to be said about a man who is willing to bend a law in order to save an entire city, or even an entire planet, and is yet unwilling to bend the same law in order to save the just the seven of us!"
"What's that, Dr. Smith?"
"I would gladly tell you, my boy, but I'm afraid you're too young to hear it!"

Ah, so you want to include other universes.
I like the idea of using established Star Trek canon.
There are planets that are "Earth, except X" such as "Earth but Rome never fell" or "Earth but anvilicious American vs Chinese society"

Hmm. How about this idea.

The Jupiter II was an early attempt at using warp drive (hence their ability to visit distant solar systems without refueling) but because it was a prototype they suffered relativistic effects: for them it's been a few years, for the rest of the galaxy, centuries.

They encounter a planet that looks just like Earth, although the stars are wrong. It's Batman's Earth. The Enterprise would come across the planet as part of their exploration mission and deduce what happened. As humans from their Earth caused an interference, they feel justified under the PD to balance it by covertly increasing Batman's equipment to levels normally implausible for his planet's level of development. And boy, won't the Green Hornet be jealous. :)

Now, if you really want to have fun with a shared universe, perhaps the villains plan to attack a government time travel facility (Time Tunnel). The adventure ends up in the Old West, and one scientist, Artemus Gordon, decides to stay behind with his knowledge of future technology to protect the timeline.

And maybe Cpt Robinson asks Kirk if they ever found out what happened to the Spindrift... (Land of the Giants).

But since you're going to focus on character interactions, the actual explanations can likely just be handwaved away.