Pokemon following you around like in Yellow,Hg,SS: I wouldn't mind this, but if it did return then I'd want it to be optional. Liked it in Yellow and at first in HG/SS but then got quickly sick of it.
Berry Trees Back: Not really bothered, never replanted berries anyhow.
New Battle system (6 on 6, etc.): Definitely not! I'm not even a big fan of triple and rotation battles, too much pokemon on the field.
Multiple Regions: Nope! Stick to one region, Kanto in G/S/C/HG/SS was just unnecessary IMO.
Battle Frontier return: Would love the Battle Frontier to return, more like the Emerald one.
New Starter types: I'd prefer the formula of Grass/Water/Fire not to be messed with, but if they did it right I guess I'd be open to change.
Dark type Gym Leader: Yes to this! Don't know why they haven't done it already, but Gen VI would be the perfect opportunity.
Tournament instead of elite four: I want the elite four to remain untouched. If it ain't broken don't fix it, lets leave the tournament style league to the anime (or postgame challenge).
Return of team rocket: Team Rocket aren't my favourite villians, but I would love to see what story they could make up for their return, maybe make them a bit more threatening.
New eeveelutions: I'm open for more eeveelutions, preferably a flying or ghost one like others have said.
New story - Not the old ten year old sets out to be champ and stop bad guys): Would agree with this to some extent. I liked the way B/W have mixed up the story a bit, but I'm sure more could be changed without altering the system. If that makes sense... :p