I would assume ether nothing or that her power would become amplified to painful levels that could cause her to assimilate powers of those around her regarldess of touch.

Well nothing really, I mean Peter's power is not the same exact power as Rogues.
 
Rogue's power hurts the person, and he only keeps the power for a limited time, and she aslo gets memories from the person.
 
Peter only replicates the power until he copies another one and it replaces the current one.

@Power NeXus said:

Seriously. If Rogue touched someone with the exact same powers as her, what would happen?

rogue has the abilitiy to absorbs someones life force and that consists of everything that they are. nearly everything has life force thus her power would work on nearly everything/ everyone except for those beings that can resist her powers, such as silver surfer.

if rougue touch peter petrelli enough she would take his empathic mimicry for a short time as well as start to take the rest of them depending on how long she holds on. she would also absorb his personality, skills, memories, habits. pretty much everything that makes him who he is ( other than his physical body)

I imagine he'd get a bit aroused. I mean c'mon, Rogues pretty hot.