Some psychic perks wouldn't be far off for a PC who is a http://fallout.wikia.com/wiki/Psyker.

A perk where you can do http://en.wikipedia.org/wiki/Remote_viewing where you can step out of your body with your mind and move through closed doors to explore for a bit, undetected, would be very useful.

Also, http://en.wikipedia.org/wiki/Psychometry_(paranormal) would be useful to let you look into the past when you touch certain objects, so you can relive the pre-war days, or a more recent past to find out about an NPC or faction.

And http://en.wikipedia.org/wiki/Clairvoyance can give you an extra boose to your Perception skills and warn you of danger earlier.

Can be other examples that are too many to list, but if creative it can be a nice implementation to any Fallout game.

Okay, I'll give you that one. Thats okay

I think this would be far too much of a distraction in fallout. As its only unlockable by a perk, the information would have to be conveyable by other routes. That said, a psychomentry based adventure game invetigating a murder could be fun.

That one is surplus to requirements. There are perks and devices that can achieve the same thing without the addition of a new perk required.

Well I said there were many possibilities of psychic ability implementation. I only listed a few on the top of my mind that sounded promising, but I'm sure there are better ones.