It's like Margaritaville but with Schnapps.

What Might Have Been

Forever Lost. 

  So assuming that the Sekkari AI downloaded itself into Atlantis' mainframe with the help of Atlantis' AI, it could then learn in what way it could best "pay John back" and help ease his mental torture.  The two AIs would conspire to make John happy by giving him back his best friend, who is spending time with Dr. Keller, who refuses to even share him with his team.  So, hiding their activities from the sensors, they make Jennifer look insane, while still protecting the inhabitants of the city.  They even get her thinking that she's had conversations with Rodney's teammates, especially John Sheppard.  At first people almost believe her, because she's Jennifer and she's doesn't have a vindictive bone in her body (whereas John Sheppard can be a cold stone killer).  Which makes people feel really bad when they find that she's, at the very least, crazy.  Eventually, she could either kill herself, have an accident, or possibly she tries to kill John Sheppard, and Ronon or Rodney have to stop her, and she ends up dead instead.  Especially if it's Rodney, he could have the realization then that he'd do anything for John Sheppard. 

Or maybe John gets desperate.  Jennifer Keller isn't only stealing his best friend, she's decided to change everything about him.  So he dusts off his Black Ops training and kills her in cold blood.  If Atlantis is helping him cover it up, he could even take his time, and explain to her WHY she's dying.

In Brain Storm:  FREEZE LIGHTNING!  She gets hit & (oh so sadly) dies.  Or she freezes to death and Rodney is unable to save her.  (Later, John will comfort Rodney by looking into the situation for him and finding that it looks like she'd been dead for 30 minutes by the time he got to her, so it wasn't his fault, because he had to fix Malcom Tuney's mistake before he could go rescue her--and the reason she ended up stuck was somehow her fault, as in if she had made a better choice, or kept from being somewhere Rodney warned her against, she would have bene fine.)

Infection: Oops!  Killed by her own retro-virus; a rabid former drone eats her face off.  :)  Todd could even help her die, as a favor for Sheppard. 

Identity:  Dies in Neva's body---again John & the team can comfort Rodney with the fact that she shouldn't have been touching things--Ronon could even say that John's not that stupid. 

Enemy at the Gate:  is there some way for her to fall over the railing and die?  That would be awesome.

Or maybe instead it's after the ending, probably back in Pegasus, where Rodney will be forced to choose between his fiancee and the man who is his best friend--he can save only one.  And even though he's been blowing Sheppard off left and right, he chooses John.  John wasn't expecting to be chosen, infact he had a sad smile as he wished Rodney well in life and said "good bye" with dignity.  Whereas Jennifer was expecting to be chosen, and was even a bit smug, gloating as John first looked resigned and then said his goodbye.  Rodney, who would be very conflicted, utterly saddened that he's been put in this situation, would see her and realize she's not worth killing his friend for.  John, shocked to be alive, thanks his friend, and expresses his sincere condolances.  Rodney might even find out later that Jennifer was terrorizing John over Rodney's choosing her (and Rodney had no clue there was an option between the two, even though she occasionally made it sound that way--she even blamed Rodney's being uncomfortable with John's attraction to him as being the reason he's been so absent from team bonding rituals). 

Or Jennifer Keller could be arrogant, and accidentally poison herself as she's experimenting with something.

Or, she could insist that she and Rodney move back to Earth, and then she gets hit by a truck!

Or maybe she's in the gateroom, and she's just blonde enough to be standing too close to the wormhole?

I'm sure there are dozens of other ways for her to die, maybe I'll add more later.  :)