I want it open ended like Grand Theft Auto, where you can freely explore the enviroments for fortune and glory. I would like to see KOTOR style conversation options that could change the course of the story. And expand on the Emperor's Tomb fighting engine. I don't know exactly what genre that would be, but it would make for some sweeet gaming.
Another point and click adventure would be great but those seem to be a dying trend (unfortunately). However, I really like the adventure/action feel of Emperor's Tomb and I would love to see another game like that, although they could add more of the elements in the poll. Allow Indy to roam more freely, upgrade and buy new gear and equipment, talk and interact with people, add more puzzles, etc. Anything's possible and I'm anxious to hear what LucasArts plans to do with the next Indy game.
And by the way, thanks Aaron H for making all these new threads. You're certainly breathing new life into some of these topics.
Seriously, I think they should hire 1) an archaeologist 2) a screenwriter and 3) a puzzle/treasure hunt expert. And actually make an intelligent game for once (I mean a full immersion Indiana Jones experience. I don't mean lame point and click "puzzles" like FoA).
It definitely should not be like a first person shooter, but I'd like to see more gun action and less fists action. Fists are just like button mashing and it's hard to get the feel right.
I would like to see a shootout scene like in RotLA, i.e. one with more variety than the ET or IM shootouts. While ET allowed you to use cover, all you had to do was start shooting right when the enemy emerged from cover.