It's happened 12 times in the 100-plus year histories of the two races. The last one to do it was Marco Pantani in 1998, but I'm a little hesitant to hang my hat on him. Previous to him, Miguel Indurain did it two years in a row, in 1992 and 1993.
The last two seasons, we've seen dominant Giro winners (Menchov was dominant on the mountains, Basso was more dominant tactically) who have flopped spectacularly at the Tour de France. Menchov was never in contention last year. Basso seemed ok for a possible top 10 this year until the stage to Pau, when he finished in the second gruppetto. Well, at least he beat Robbie McEwen home...
Supposedly Alberto Contador has told Giro director Angelo Zomegnan that he'll ride the 2011 Giro, likely with this goal in mind. If anyone can do it, Contador would have to be the man. But I think it's a much steeper task than the Giro/Vuelta a España double he pulled off in 2008. The Dolomites are far tougher than the Sierras, I don't think anyone would doubt that. Where the Alps and the Pyrenees rank among them really depends on which climbs the Tour chooses to visit in a particular year. Certainly the Dolomites were harder than the Alps this year, and you could make the case that they were harder than the Pyrenees (the Peyresourde/Aspin/Tourmalet/Aubsique stage was a beast, but I think it falls short of the Livigno/Deia/Foscagno/Gavia/Tonale stage from the Giro. Maybe if it had ended at the Col d'Aubisque a better comparison could be drawn)
It depends a little on the rider, too, I guess. Menchov and Basso both fell flat on their faces (though, fortunately, not literally like Jens Voigt), but in the past two seasons Cadel Evans has found himself getting stronger in his second Grand Tour. He too had a forgettable '09 Tour, but backed it up with a podium finish in the '09 Vuelta. He had a solid '10 Giro, and if he hadn't broken his elbow, there's no telling how well he could have done in the Tour. Not the win, certainly, but a podium wasn't out of the question.
I guess I don't have much of a summary point, but this has been on my mind lately. If Contador does it, chapeau to him and we'll know, beyond any lingering little shadow of a doubt that we're looking at a living legend in the sport. Frankly, if he does it and therefore has the confidence to do it two years, three years, four years in a row, it's kind of staggering to think how many Grand Tours he might win before there's no more watts left in those pedals. Eddy Merckx won 11 Grand Tours in 11 years. Contador's four days away from his fifth in four years.