After 75+ years, it looks like Batman is ready to tie the knot with long time on again/off again love interest (and all around badass), Catwoman. and I couldn't be happier. The couple has had their fare share of shit through the years, so I'll just highlight the key moments between the two.
Selina Kyle made her comic book debut in Batman #1 in 1940. Of course back then she was simply known as The Cat, a cat burglar who Batman caught and let go. The dialogue is a little, uh, weird (yes Batman really did say that) but never the less, this is an important moment for our duo.
As far as a first kiss goes, that depends on how you look at it. The Cat and Batman did share a kiss in Batman #3, but then again when she wore her new Cat-Woman costume in Batman #10. In issue 15 she decides she wants to change her ways, but we all know that never happens. It's also interesting to see how Catwoman's costume evolved in a handful of issues, but that's a topic for another day.
It wasn't until the 70's however, when Bruce and Selina started to pursue a relationship. At this point, I could go off into the Earth 2 where Batman and Catwoman did marry each other in DC Super Stars #17, which also introduced Batman and Catwoman's daughter–Huntress.
The two have shared tender kisses, and nearly bare all sex scenes in the comics. But my absolute favorite representation of the two characters would have to be in Batman Returns. Selina is a down trodden secretary for Maxwell Shreck, the cold hearted tycoon. After Selina becomes Catwoman, she is a femme fatale hellbent on revenge. But Selina falls in love with Bruce, they realize who they are, and feelings become rightfully conflicted. It's actually strangely beautiful watching Michelle Pfeiffer's eyes well up with tears as she woefully asks if they have to start fighting now. The couple was doomed to fail however, and we never know if that universe's Batman and Catwoman have a happily ever after.
Personally, I don't think this engagement/marriage will last. It'll likely get re-written a thousand times over, but it's nice to see this between the two. I just hope it doesn't turn the comic into some awful gimmick.