I like the idea of Cersei and Jaime being Targs for many of the reasons already stated here: the idea of Tywin raising them without realizing it is delicious... almost as delicious as Tywin knowing and being unable to find a way around it, especially once Tyrion is born. Plus, the whole "incest = genetic?" thing would amuse me, and Cersei certainly has some of the insanity that the Targs are famous for. The idea of her ending up as crazy as Aerys while Jaime goes on to try to redeem himself (which is how I see things going), and ending up as honorable as his half-brother Rhaegar is quite delightful, too.
I guess I'm the only one who doesn't see the appeal, storyline wise, for having all of the Lannister kids turn out to be Targaryens.
This seems to absolve Tywin of kinslaying (after all, Tywin's not really his father), absolve Jaime and Cersei of committing incest (after all, they're Targs), strip Cersei's descent into madness of any sort of poetic justice (hey, she's a Targ, half of them go crazy anyway), absolve Tywin of the horrible way he treated Tyrion (Aerys raped his wife, who can blame him for being such an awful father), and increase opportunities for Jaime to become an even bigger fan favorite. Hey, maybe we'll even find out that Aerys married Joanna in secret so that Jaime actually has a claim to the Iron Throne himself.
On top of that, I just don't think there's much support for it in the books. Aerys raped the wife of his Hand on two separate occasions and not a whisper or hint from anyone about it? Not even a throwaway reference to Joanna making visits to King's Landing? Or even comments about Aerys being a womanizer along the lines of Aegon IV. I'm just not buying it. The only thing we hear about the early years of Aerys' reign, and, given the conception of Jaime and Cersei, his raping Joanna would have to have occurred during the early years of his reign, was that he was charming and generous but prone to "lapses". I never interpreted "lapses" as raping noblewomen married to the most powerful members of his Small Council.