1) Which is the richest/deepest beat em up you've played? I'm not talking philosophically but more about being able to do a lot within the game.
As far as sheer number of moves you can perform, probably the
Guardian Heroes games. Even
Advance Guardian Heroes was impressive with how many moves they crammed into two buttons and a D-pad. Plus the barrier-reflect move you perform with R calls back to one of Treasure's more interesting design philosophies of giving you the bigger advantage the more you put yourself in harm's way, if not outright requiring you to do so in order to progress (Mischief Makers and Bangai-O both do the same thing to great effect).
2) What is the most fun as an experience?
Seconding
Castle Crashers here. The variety of settings and characters, the situations you find yourself in, and the sheer style with which it's all pulled off all come together in a way that's like nothing else out there. Even the introduction to the first boss gave me an impression of "holy shit, these guys aren't playing around."
3) What, for better or worse, is the most experimental beat em up you've played?
This is probably a boring answer, but gameplay wise,
Guardian Heroes. Turning what could have normally been a "hit punch button to win" type affair into basically "Street Fighter but with hundreds of dudes" will never not feel like an inspired move to me.
As far as setting,
Pu·Li·Ru·La, simply because of how insane it gets.
4) I remember a LOT of the games I played in the early 90s were licensed. What IP would make an awesome licensed game?
Adventure Time! I feel like Adventure Time could lend itself well to a lot of genres.
OOO!!! Or maybe a beat-em-up set in the Darkstalkers universe! One with the same 2D style as the fighting games would be fucking bonkers.
5) What out of print licensed game would you be happy to buy? There's a specific one that comes to my mind but I feel like there are a few.
The big three that I can think of are
The Simpsons,
Alien VS Predator, and yeah
Scott Pilgrim VS the World.
6) What genre or genre elements would you like to see mashed up with the beat em up?
If I have to pick one, maybe something with some very light RTS elements. It might be fun to have a little group of minions you can boss around while you're smacking goons around. Maybe they could help you combo attack against a particularly tough enemy, help with crown control, support you with healing or buffs, or even build little structures like walls or pit traps or whatever. Don't know how you'd pull off something like that well, though.
I feel like I'm basically describing Final Fantasy XV or Dragon's Dogma or something with half of this. I don't know.